{"id":24595,"date":"2023-02-15T11:32:11","date_gmt":"2023-02-15T11:32:11","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=24595"},"modified":"2023-02-16T05:24:15","modified_gmt":"2023-02-16T05:24:15","slug":"vertices-faces-and-edges","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges","title":{"rendered":"Vertices, Faces And Edges"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-60b188de-fb87-43b2-b10f-7a66839d7e2a\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#4-what-are-vertices->What are Vertices?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#21-what-are-faces>What are Faces?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#27-what-are-edges>What are Edges?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#34-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#35-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges#36-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-what-are-vertices-faces-edges\">What Are Vertices, Faces, Edges?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Every geometric shape is composed of different parts such as vertices, faces, edges. We come across different objects with rectangular faces, circular faces, cubic faces, diamond faces, triangular faces, etc. We also know many objects that have sharp corners and edges. We will learn about vertices, faces, edges of different plane shapes and geometric shapes. First, let\u2019s understand plane shapes and solid shapes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"322\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-1.png\" alt=\"Vertex, edge, and face example in a cube\" class=\"wp-image-24602\" title=\"Vertex, edge, and face example in a cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-1-300x156.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-sides-and-vertices-in-a-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_sides_vertices_pt.png\" alt=\"Count Sides and Vertices in a Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Sides and Vertices in a Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-the-faces\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_faces_pt.png\" alt=\"Count the Faces Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count the Faces Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-the-vertices\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_vertices_pt.png\" alt=\"Count the Vertices Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count the Vertices Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/determine-sides-and-vertices\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_sides_vertices_pt.png\" alt=\"Determine Sides and Vertices Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Determine Sides and Vertices Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-shapes-on-the-basis-of-faces\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_shapes_based_on_faces_pt.png\" alt=\"Identify Shapes on the basis of Faces Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Shapes on the basis of Faces Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-shapes-on-the-basis-of-surfaces\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_shapes_based_on_surfaces_pt.png\" alt=\"Identify Shapes on the basis of Surfaces Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Shapes on the basis of Surfaces Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-shapes-on-the-basis-of-vertices\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_shapes_based_on_vertices_pt.png\" alt=\"Identify Shapes on the basis of Vertices Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Shapes on the basis of Vertices Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"eplus-wrapper wp-block-heading\" id=\"1-plane-shapes-\"><strong>Plane Shapes<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any two-dimensional shape that is closed and flat is known as a plane shape. Plane shapes do not have thickness. Different plane shapes have different characteristics, like the number of vertices, the number of sides, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Some examples of plane shapes are circles, triangles, rectangles, ovals, polygons, etc.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"362\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-2.png\" alt=\"Examples of plane shapes\" class=\"wp-image-24604\" title=\"Examples of plane shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-2.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-2-300x175.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"2-solid-shapes-\"><strong>Solid Shapes<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any three-dimensional objects with length, breadth, and height are known as solid shapes. Pyramids, cuboids, cubes, and cones are examples of three-dimensional shapes. Their surfaces are called faces.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-3.png\" alt=\"Examples of solid shapes\" class=\"wp-image-24605\" title=\"Examples of solid shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-3.png 622w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-3-300x178.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Examples:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A sphere is a solid figure with only one curved face, no edges, and no vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cone has 2 faces: one curved face and another flat circular face but only one vertex and edge each.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Another example is a cylinder that has three faces, with two edges but no vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let\u2019s understand what faces, vertices, and edges are.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"3-dimensions-of-a-shape-\"><strong>Dimensions of a Shape<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Dimensions in mathematics are&nbsp;<strong>the measure of the size or distance of an object or region or space in one direction<\/strong>. In simpler terms, it is the measurement of the length, width, and height of anything.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-4-1.png\" alt=\"Dimensions of a shape\" class=\"wp-image-24725\" title=\"Dimensions of a shape\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-4-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-4-1-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A point has no dimension.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A line is one dimensional since it only has length.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube is three dimensional since it has length, breadth, and height.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"4-what-are-vertices-\"><strong>What are Vertices?<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Look for the points where two or three lines meet, like the corner of a cardboard sheet or the corner of a gift box. These are examples of vertices. The point where three edges or lines meet is known as the vertex. The plural form of a vertex is vertices.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-5.png\" alt=\"Examples of vertices\" class=\"wp-image-24607\" title=\"Examples of vertices\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-5-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand this with an example: A cube has 8 corners or vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-6.png\" alt=\"Vertices of a cube\" class=\"wp-image-24608\" title=\"Vertices of a cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-6.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-6-300x174.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The common endpoint where two or more rays or line segments meet is called a <strong>vertex<\/strong>. The plural of vertex is \u201c<strong>vertices<\/strong>.\u201d Vertices are denoted by capital letters.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"281\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-7.png\" alt=\"Vertex of a ray and line segment\" class=\"wp-image-24609\" title=\"Vertex of a ray and line segment\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-7-300x136.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An <strong>angle<\/strong> is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the<strong> vertex of an angle<\/strong>. We can see that we are looking at the \u201ccorner\u201d of the angle to see the vertex. Vertices are sometimes also called corners.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"315\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-8.png\" alt=\"Vertex of an angle\" class=\"wp-image-24610\" title=\"Vertex of an angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-8-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"5-vertices-of-2d-shapes\">Vertices of 2D Shapes<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2-dimensional shapes<\/strong> are flat shapes which have only two dimensions, length and width. Triangle, rectangle, circle are a few examples of 2D shapes. Simple, closed 2D shapes made up of only straight lines are called <strong>polygons<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The line segments that make the polygon are known as <strong>sides or edges<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The point where adjacent sides meet is called <strong>vertex<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Different shapes have different numbers of vertices. Let us see vertices of some 2D shapes.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"6-vertices-of-a-triangle\">Vertices of a Triangle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Triangle<\/strong> is a three-sided 2D shape or polygon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle is made up of three line segments or sides. A triangle has 3 sides, 3 vertices and 3 angles. A triangle is denoted by the symbol&nbsp; $\\Delta$&nbsp; .<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"428\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-9.png\" alt=\"Vertices of a triangle\" class=\"wp-image-24611\" title=\"Vertices of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-9-300x207.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In&nbsp; &nbsp;$\\Delta$ &nbsp; ABC, (AB, BC), (BC, CA) and (CA, AB) are adjacent sides of the given triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;\u201cA\u201d, \u201cB\u201d, \u201cC\u201d are the three vertices since the adjacent sides meet at these points.&nbsp;<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"7-vertices-of-a-square\">Vertices of a Square<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Square<\/strong> is a four sided 2D shape or polygon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A square is made up of four line segments or sides. Adjacent sides of a square meet at a point known as<strong> vertex<\/strong>. A square has four sides, four vertices and four angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"561\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-10.png\" alt=\"Vertices of a square\" class=\"wp-image-24612\" title=\"Vertices of a square\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-10-300x271.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(AB, BC), (BC, CD), (CD, DA) and (DA, AB) are adjacent sides of the square.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, in square ABCD, \u201cA,\u201d \u201cB,\u201d \u201cC,\u201d and \u201cD\u201d are the four vertices.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"8-vertices-of-a-rectangle\">Vertices of a Rectangle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Rectangle<\/strong> is a four sided 2D shape or polygon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A rectangle is made up of four line segments or sides. Adjacent sides of a square meet at a point known as<strong> vertex<\/strong>. A square has four sides, four vertices and four angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"699\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-11.png\" alt=\"Vertices of a rectangle\" class=\"wp-image-24613\" title=\"Vertices of a rectangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-11.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-11-266x300.png 266w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(AB, BC), (BC, CD), (CD, DA) and (DA, AB) are adjacent sides of the rectangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, in the rectangle ABCD, \u201cA,\u201d \u201cB,\u201d \u201cC,\u201d and \u201cD\u201d will be the four vertices.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"9-vertices-of-a-pentagon\">Vertices of a Pentagon<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Pentagon<\/strong> is a five sided 2D shape.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagon is made up of five line segments or sides. Adjacent sides of a pentagon meet at a point known as<strong> vertex<\/strong>. A pentagon has five sides, five vertices, and five angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"506\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-12.png\" alt=\"Vertices of a pentagon\" class=\"wp-image-24614\" title=\"Vertices of a pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-12.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-12-300x245.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(AB, BC), (BC, CD), (CD, DE), (DE, EA) and (EA, AB) are adjacent sides of the pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, in pentagon ABCDE, \u201cA,\u201d \u201cB,\u201d \u201cC,\u201d \u201cD,\u201d and \u201cE\u201d will be the five vertices.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"10-vertices-of-an-irregular-shape\">Vertices of an Irregular Shape<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The figure shown is of a pentagon with unequal sides. A polygon with unequal sides is known as an<strong> irregular polygon<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, too, a vertex is formed when two adjacent sides meet.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, in the given image, we have an irregular pentagon that has five vertices and five sides.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"498\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-13.png\" alt=\"Vertices of an irregular pentagon\" class=\"wp-image-24615\" title=\"Vertices of an irregular pentagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-13.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-13-300x241.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the given irregular pentagon ABCDE, \u201cA,\u201d \u201cB,\u201d \u201cC,\u201d \u201cD,\u201d and \u201cE\u201d are the five vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(AB, BC), (BC, CD), (CD, DE), (DE, EA) and (EA, AB) are adjacent sides of the pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Look at the table:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"280\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-14.png\" alt=\"Relationship between sides and vertices\" class=\"wp-image-24616\" title=\"Relationship between sides and vertices\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-14.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-14-300x135.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can see that t<strong>he number of vertices is always equal to the number of sides of a polygon.<\/strong><\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"11-vertices-of-a-circle\">Vertices of a Circle<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>circle <\/strong>is a 2D shape consisting of all points in a plane that are at a given distance from a given point, the center.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"399\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-15.png\" alt=\"Circle\" class=\"wp-image-24617\" title=\"Circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-15.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-15-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A circle has infinite points on it but has zero vertices as vertex is a point where line segments or rays meet and circle has no line segments or rays.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"12-vertices-of-3d-shapes-\"><strong>Vertices of 3D Shapes<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">3D stands for 3-dimensional or three-dimensional. <strong>Three-dimensional shapes<\/strong> are shapes which have three dimensions: length, width, and height. Cube, pyramid, and cone are few examples of 3D shapes.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">3D shapes have faces, edges and vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>face<\/strong> is a flat or curved surface on a 3D shape.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An<strong> edge<\/strong> is where two faces meet.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>vertex <\/strong>is a point where edges meet.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-16.png\" alt=\"Face, edges, and vertices of a 3D shape\" class=\"wp-image-24618\" title=\"Face, edges, and vertices of a 3D shape\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-16.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-16-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Different 3D shapes have different numbers of vertices. Let us see vertices of some 3D shapes.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"13-vertices-of-a-cube\">Vertices of a Cube<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube is a three-dimensional solid bounded by six square faces, with three faces meeting at each vertex.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube has 8 vertices. 7 are visible here and one is hidden.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube has 6 faces and 12 edges.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-17.png\" alt=\"Vertices, faces, and edges of a cube\" class=\"wp-image-24619\" title=\"Vertices, faces, and edges of a cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-17.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-17-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can see in the given figure that the point where AB and AC meet is one of the vertices of the cube. Similarly, where two or more edges meet on the cube, we call that point the vertex.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"14-vertices-of-a-cuboid\">Vertices of a Cuboid<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cuboid is a three-dimensional solid bounded by six rectangular faces, with three faces meeting at each vertex.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"507\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-18.png\" alt=\"Vertices of a cuboid\" class=\"wp-image-24620\" title=\"Vertices of a cuboid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-18.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-18-300x245.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the cuboid shown A, B, C, D, E, F, G, and H are the 8 vertices of the cuboid.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cuboid has 8 vertices, 6 faces and 12 edges.&nbsp;<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"15-vertices-of-a-prism\">Vertices of a prism<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>prism <\/strong>is a 3D shape for which the top and bottom faces are congruent polygons, and all other faces are rectangles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In a prism, the number of vertices will be equal to twice the number of vertices in one face.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Number of vertices in a prism $= 2 \\times$ Number of vertices in one face.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s take an example of a triangular prism. We know that a triangle has 3 vertices.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the number of vertices in a triangular prism $= 2 \\times$ Number of vertices in a triangle&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 2 \\times 3 = 6$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"531\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-19.png\" alt=\"Vertices, faces, and edges of a triangular prism\" class=\"wp-image-24621\" title=\"Vertices, faces, and edges of a triangular prism\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-19.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-19-300x257.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the triangular prism shown A, B, C, D, E and F are the 6 vertices of the prism.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangular prism has 6 vertices, 9 edges along with 2 triangular faces (base) and 3 rectangular faces.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"16-vertices-of-a-pyramid\">Vertices of a pyramid<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>pyramid<\/strong> has a polygonal base and flat triangular faces that are joined at a common point called the <strong>vertex<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In a pyramid, the number of vertices will be equal to one more than the number of vertices in the base.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Number of vertices in a pyramid $= 1 +$ number of vertices in the base<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s take an example of a square pyramid. We know that a square has 4 vertices.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, the number of vertices in a square pyramid $= 1 +$ Number of vertices in a square<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 1 + 4 = 5$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"578\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-20.png\" alt=\"Vertices, faces, and edges of a square pyramid\" class=\"wp-image-24622\" title=\"Vertices, faces, and edges of a square pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-20.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-20-300x280.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the square pyramid shown A, B, C, D and E are the 5 vertices of the pyramid.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A square pyramid has 5 vertices and 8 edges, with 1 square face (base) and 4 triangular faces.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"17-special-types-of-3d-shapes-and-their-vertices\">Special Types of 3D Shapes and Their Vertices<\/h2>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"18-vertices-of-a-cone\">Vertices of a Cone<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>cone<\/strong> is a three-dimensional figure that has a flat surface and a curved surface, pointed towards the top at the vertex. It\u2019s a special type of figure where the base is circular and has only one vertex at the top.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-21.png\" alt=\"Vertices, faces, and edges of a cone\" class=\"wp-image-24623\" title=\"Vertices, faces, and edges of a cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-21.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-21-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the cone shown, A is the vertex of the cone.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cone has 1 vertex and 1 circular edge.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cone has 2 faces, 1 flat circular surface and 1 curved face.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"19-vertices-of-a-cylinder\">Vertices of a Cylinder<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>cylinder<\/strong> is a 3D shape consisting of two parallel circular bases that are joined by a curved surface. It has 2 circular bases that means two circular edges which are parallel and no straight lines which meet these edges. Therefore, a cylinder has no vertices.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"573\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-22.png\" alt=\"Vertices, faces, and edges of a cylinder\" class=\"wp-image-24624\" title=\"Vertices, faces, and edges of a cylinder\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-22.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-22-300x277.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder has no vertex as it has no straight edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder has 3 faces, 2 flat, and 1 curved face.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder has 2 circular edges.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"20-vertices-of-a-cphere\">Vertices of a Cphere<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A <strong>sphere<\/strong> is the set of all points in three-dimensional space lying at the same distance from a given point, center. A sphere has no edges or straight lines and only one circular surface, therefore, a sphere has no vertices.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"421\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-23.png\" alt=\"Sphere\" class=\"wp-image-24625\" title=\"Sphere\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-23.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-23-300x204.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"21-what-are-faces\">What are Faces?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A face of a solid can be defined as every single flat surface of a solid. It forms part of the boundary. In any geometric solid that is made of flat surfaces, each flat surface is called a face.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any two dimensional shape has only one flat face.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"22-faces-of-a-cube\">Faces of a Cube<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube has 6 square-shaped faces.&nbsp;<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"23-faces-of-a-cuboid\">Faces of a Cuboid<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cuboid has 6 rectangular-shaped faces, where the opposite faces are the same.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"24-faces-of-a-square-pyramid\">Faces of a Square Pyramid<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A square-based pyramid has a square face as a base with four triangular faces on its sides.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"25-faces-of-a-cone\">Faces of a Cone<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cone\u2019s base is a flat circle face with one curved face wrapping around its base.&nbsp;<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"26-faces-of-a-sphere\">Faces of a Sphere<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A sphere has no flat faces but one complete curved face.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"693\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-24.png\" alt=\"Faces in different solids\" class=\"wp-image-24626\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-24.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-24-268x300.png 268w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"27-what-are-edges\">What are Edges?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Edges are line segments where two faces of a solid meet. Edges on a 2D shape connect two vertices.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An edge is a line that joins the corners or edges of a given shape or surface. There is a difference in how we can define <strong>edges<\/strong> for a two-dimensional and a three-dimensional figure.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"28-edges-in-a-2d-shapes\">Edges in a 2D Shapes<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any line that makes up the shape&#8217;s sides are its edges for a two-dimensional flat shape. An edge is a line segment between two faces of a solid or a line segment on a boundary?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a square ABCD as shown below. A square is a 2D shape. In a 2D shape, any bounding straight edge is also called a side.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"502\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-25.png\" alt=\"Sides in different 2D shapes\" class=\"wp-image-24627\" title=\"Sides in different 2D shapes\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-25.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-25-300x243.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"29-edges-in-a-3d-shapes\">Edges in a 3D Shapes<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For a three-dimensional solid, edges are those line segments where any flat sides of the object meet. We often refer to the <strong>edges <\/strong>as the shape&#8217;s sides. Accordingly, different shapes have different numbers of edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, a cube has 12 edges.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"375\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-26.png\" alt=\"Number of edges, vertices, and faces in a cube\" class=\"wp-image-24628\" title=\"Number of edges, vertices, and faces in a cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-26.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-26-300x181.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder is a 3D shape, and it has 2 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A sphere is a perfect round, which is why it has no edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A tetrahedron has 6 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cone is a unique shape with only one edge, vertex and face.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"30-edges-in-real-life-\"><strong>Edges in Real Life<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are plenty of real-life examples of edges in some daily objects. We look at them almost daily, and it is easy to find them around us.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">A microwave in the shape of a cuboid has several edges. The edges may be curved or sharp straight.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">A birthday hat is conical in shape. It has only one edge.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Just like a cube, a rolling dice has 12 edges.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"31-difference-between-edges-and-vertices-\"><strong>Difference Between Edges and Vertices<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us see the difference between edges and vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An edge of a 3D shape is where two faces meet. They are the line segments or curved lines which make the 3D shape. But a vertex is the point where two or more edges or line segments meet.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An interesting case is that of a cylinder which has 2 edges but both of them are circular so they do not meet at a singular point, making the cycling devoid of any vertices.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"425\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-27.png\" alt=\"Difference between vertices and edges\" class=\"wp-image-24629\" title=\"Difference between vertices and edges\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-27.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-27-300x206.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"32-euler%E2%80%99s-formula\">Euler\u2019s Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A three-dimensional shape made up of polygonal faces is known as a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polyhedron\"><strong>polyhedron<\/strong><\/a>. Examples of polyhedrons are cube, prism, pyramid and so on.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The relationship between vertices, edges and faces for polyhedrons can be given by Euler\u2019s formula.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Euler\u2019s formula says, in a polyhedron, the number of vertices (V) and faces (F) together is exactly two more than the number of edges (E).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\text{V} + \\text{F} = 2 + \\text{E}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\text{V} + \\text{F} \\;\u2212\\; \\text{E} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Euler\u2019s formula is satisfied by all polyhedrons. We can also say that a 3D shape is a polyhedron if it satisfies Euler\u2019s formula.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> Let us verify Euler\u2019s formula for a cube.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-28.png\" alt=\"Cube\" class=\"wp-image-24630\" title=\"Cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-28.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-28-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cube has 8 vertices, 12 edges and 6 faces.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">i.e. $\\text{V} = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;$\\text{E} = 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\text{F} = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Euler\u2019s formula:<\/strong>&nbsp; $\\text{V} + \\text{F} \\;\u2212\\; \\text{E} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$8 + 6 \u2013 12 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $2 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, Euler\u2019s formula is verified. Cube is a polyhedron.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2:<\/strong> Square pyramid<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-29.png\" alt=\"Square pyramid\" class=\"wp-image-24631\" title=\"Square pyramid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-29.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-29-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this square pyramid, there are<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">4 triangular faces and 1 square face $= 5$ faces<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">1 vertex at the top and 4 vertices at the base $= 5$ vertices<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">4 slant edges and 4 edges at the base $= 8$ edges<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, using Euler&#8217;s formula,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5 + 5 &#8211; 8 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You can also try this formula on other platonic solids, such as octahedrons, tetrahedrons, etc.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"33-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learnt about vertices, edges, and faces of different shapes. Let\u2019s solve a few examples for better understanding.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"34-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. How many vertices are there in a hexagon?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> &nbsp;As a hexagon is a 6-sided polygon, it will also have 6 vertices. In this hexagon, A, B, C, D, E, F are the vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"339\" height=\"339\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30.png\" alt=\"Hexagon\" class=\"wp-image-24632\" title=\"Hexagon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30.png 339w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-30-120x120.png 120w\" sizes=\"auto, (max-width: 339px) 100vw, 339px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. How many vertices does a rectangular prism have?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A rectangular prism has 8 vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"175\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-31.png\" alt=\"Vertices of a cuboid\" class=\"wp-image-24633\" title=\"Vertices of a cuboid\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A, B, C, D, E, F, G, H are the vertices of the above rectangular prism.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. How many vertices does a triangular pyramid have?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangular pyramid had 4 vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"244\" height=\"264\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-32.png\" alt=\"Vertices of a triangular pyramid\" class=\"wp-image-24634\" title=\"Vertices of a triangular pyramid\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A, B, C and D are the vertices of a triangular pyramid shown above.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Verify Euler\u2019s formula for a pentagonal pyramid.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A pentagonal pyramid is a three-dimensional shape with a pentagonal base and upon which are five triangle-shaped lateral sides that meet at the vertex.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"263\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-33.png\" alt=\"Vertices of a pentagonal pyramid\" class=\"wp-image-24635\" title=\"Vertices of a pentagonal pyramid\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Pentagonal pyramid has 6 vertices<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Pentagonal pyramid has 10 edges<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Pentagonal pyramid has 6 faces<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Euler\u2019s formula:<\/strong> $\\text{V} \\;\u2212\\; \\text{E} + \\text{F} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$6 \\;\u2013\\; 10 + 6 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, Euler\u2019s formula is verified for a pentagonal pyramid.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Can you tell how many vertices a hexagonal pyramid will have, without counting?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Vertices of a pyramid $= 1 +$ Vertices of the base<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A hexagonal pyramid will have a hexagon as its base<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, Vertices of a hexagonal pyramid $= 1 +$ vertices of hexagon<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 1 + 6 = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>6. How many faces, vertices, and edges are present in a pentagonal prism?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"194\" height=\"256\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-34.png\" alt=\"Faces, vertices and edges of a pentagonal prism\" class=\"wp-image-24636\" title=\"Faces, vertices and edges of a pentagonal prism\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This pentagonal prism has 7 faces, 10 corners, and 15 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>7. How faces, vertices and edges does a tetrahedron have?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A tetrahedron has 4 flat surfaces, all of which are triangular in shape, 6 edges and 4 vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"274\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-35.png\" alt=\"Faces of a tetrahedron\" class=\"wp-image-24637\" title=\"Faces of a tetrahedron\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>8. What is the difference between a cube and a cuboid in terms of faces, vertices and edges? Explain their dimensions.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Both cubes and cuboids are three dimensional in shape with mutually right-aligned surfaces. Both shapes have 6 faces, 12 edges, and 8 vertices.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we talk about differences, then all 6 faces of the cuboid are rectangular, but all 6 faces of the cube are square.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cuboid&#8217;s length, breadth, and height are not the same, but in a cube, all the 3 dimensions are the same.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So all cubes are cuboids, but all cuboids may or may not be cubes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"250\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-36.png\" alt=\"Cube and cuboid\" class=\"wp-image-24638\" title=\"Cube and cuboid\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-36.png 571w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-36-300x131.png 300w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>9. Is a cylinder a solid shape or a plane shape? How many faces, vertices and edges does a cylinder have?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder is a three-dimensional object with two identical, circular faces at each end, one curved side and no edges or vertices.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"124\" height=\"207\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-37.png\" alt=\"Cylinder\" class=\"wp-image-24639\" title=\"Cylinder\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>10. How will you prove Euler&#8217;s Formula for a tetrahedron?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> &nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that a tetrahedron is a polygon with 4 faces, 4 vertices, and 6 edges. According to Euler\u2019s Formula, $\\text{F} + \\text{V} = \\text{E} + 2$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">$4 + 4 = 6 + 2$<\/li>\n\n\n\n<li class=\" eplus-wrapper\">$8 = 8$<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Hence Proved.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>11.&nbsp; The edge of a square is 10 feet. What will be the perimeter?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The perimeter of the square shape will be the sum of its four sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Assuming that the square is a two-dimensional shape, we know that the perimeter equals the sum of all edges of the shape.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter $= 10\\; ft + 10\\; ft + 10\\; ft + 10\\; ft = 40\\; ft$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>12. The edge of a cube is 12 cm. What will be its perimeter?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of a cube $=$ Number of edges $\\times$ Length of each edge.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, we know that number of edges in a cube $= 12$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of a cube $= 12 \\times 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Perimeter of a cube $= 144$ cm<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>13. A cube has 6 faces and 12 edges, what will be the number of its vertices according to Euler&#8217;s Formula?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of vertices will be 8.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to Euler\u2019s Formula, $\\text{F} + \\text{V} = \\text{E} + 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$6 + \\text{V} = 12 + 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\text{V} = 12 + 2 \\;\u2013\\; 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$\\text{V} = 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>14. To draw a square and a triangle on paper, how many total edges will we have to draw?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We will draw a total of 7 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A square has 4 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle has 3 edges.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, to draw a square and a triangle on paper, we have to draw 7 edges.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"35-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Vertices, Faces And Edges<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">How many vertices does an octagon have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6<\/div><div class=\"spq_answer_block\" data-value=\"1\">7<\/div><div class=\"spq_answer_block\" data-value=\"2\">8<\/div><div class=\"spq_answer_block\" data-value=\"3\">9<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8<br\/>An octagon has 8 vertices.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">How many vertices does the given irregular polygon have?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/pp2-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">7<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">9<\/div><div class=\"spq_answer_block\" data-value=\"3\">10<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 10<br\/>The given irregular polygon has 10 vertices.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/pp3-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">How many vertices does a pentagonal prism have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">10<\/div><div class=\"spq_answer_block\" data-value=\"3\">12<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 10<br\/>A pentagonal prism has 10 vertices.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/pp4-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">A polyhedron has 12 edges and 6 faces, find the number of vertices.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">6<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">10<\/div><div class=\"spq_answer_block\" data-value=\"3\">12<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8<br\/>Euler\u2019s formula is $\\text{V} \\;\u2212\\; \\text{E} + \\text{F} = 2$<br>\r\n$\\text{V} \\;\u2013\\; 12 + 6 = 2 ; \\text{V} = 8$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which of the following 3D shape has:<br>Faces: 5<br>Edges: 9<br>Vertices: 6<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Cube<\/div><div class=\"spq_answer_block\" data-value=\"1\">Tetrahedron<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangular prism<\/div><div class=\"spq_answer_block\" data-value=\"3\">Triangular pyramid<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Triangular prism<br\/>A triangular prism has 5 faces, 9 edges, and 6 vertices.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">Which among these below is Euler's formula?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\text{F} + \\text{V} \\;-\\; \\text{E} = 2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\text{F} + \\text{V} \\;-\\; \\text{E} = 3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\text{F} + \\text{E} \\;-\\; \\text{V} = 2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\text{F} + \\text{E} \\;-\\; \\text{V} = 3$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\text{F} + \\text{V} \\;-\\; \\text{E} = 2$<br\/>There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $\\text{F} + \\text{V} \\;-\\; \\text{E} = 2$ (Here, $\\text{F} =$ faces, $\\text{V} =$ vertices, $\\text{E} =$ edges)<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">7<\/span><h3 class=\"sqp_question_text\">What type of faces does a cone have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2 curved faces<\/div><div class=\"spq_answer_block\" data-value=\"1\">2 flat circle faces<\/div><div class=\"spq_answer_block\" data-value=\"2\">1 curved and 1 circular face<\/div><div class=\"spq_answer_block\" data-value=\"3\">1 triangle face and 1 circle face<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1 curved and 1 circular face<br\/>A cone has 2 faces: one curved face and another flat circle face.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">8<\/span><h3 class=\"sqp_question_text\">How many edges does a cone have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">0<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>A cone has only one curved edge.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">9<\/span><h3 class=\"sqp_question_text\">Which of the following solids has the least number of faces?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Square pyramid<\/div><div class=\"spq_answer_block\" data-value=\"1\">Rectangular pyramid<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangular pyramid<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Triangular pyramid<br\/>Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">10<\/span><h3 class=\"sqp_question_text\">If the number of faces of a cube is 6 and vertices is 8, find out the number of edges according to Euler's formula.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12<\/div><div class=\"spq_answer_block\" data-value=\"1\">14<\/div><div class=\"spq_answer_block\" data-value=\"2\">15<\/div><div class=\"spq_answer_block\" data-value=\"3\">16<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 12<br\/>According to Euler\u2019s Formula, $\\text{F} + \\text{V} = \\text{E} + 2$<br>\r\n$6 + 8 = \\text{E} + 2$<br>\r\n$14 = \\text{E} + 2$<br>\r\n$14 \\;\u2013\\; 2 = \\text{E}$<br>\r\n$\\text{E} = 12$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">11<\/span><h3 class=\"sqp_question_text\">Which of the following solid shapes do not have any edges?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Cube<\/div><div class=\"spq_answer_block\" data-value=\"1\">Triangular prism<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangular Pyramid<\/div><div class=\"spq_answer_block\" data-value=\"3\">Sphere<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Sphere<br\/>A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">12<\/span><h3 class=\"sqp_question_text\">Which of the following shapes have a curved edge?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Cone<\/div><div class=\"spq_answer_block\" data-value=\"1\">Cube<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangular prism<\/div><div class=\"spq_answer_block\" data-value=\"3\">Triangular pyramid<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Cone<br\/>A cone is the only shape out of the given options with a curved edge in the shape of a circle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">13<\/span><h3 class=\"sqp_question_text\">What do we call a point where two or more edges meet?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Vertex<\/div><div class=\"spq_answer_block\" data-value=\"1\">Edge<\/div><div class=\"spq_answer_block\" data-value=\"2\">Face<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Vertex<br\/>A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">14<\/span><h3 class=\"sqp_question_text\">If the edges of a triangle are 12 in, 14 in, and 12 in, what will be its perimeter?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">48 in<\/div><div class=\"spq_answer_block\" data-value=\"1\">38 in<\/div><div class=\"spq_answer_block\" data-value=\"2\">35 in<\/div><div class=\"spq_answer_block\" data-value=\"3\">65 in<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 38 in<br\/>The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $= 12 + 14 + 12$<br>\r\nPerimeter $= 38$ in<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Vertices, Faces And Edges\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Vertices, Faces And Edges\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many vertices 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\"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A pentagonal prism has 10 vertices.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A pentagonal prism has 10 vertices.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"10\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A pentagonal prism has 10 vertices. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/pp4-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A pentagonal prism has 10 vertices. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/pp4-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A polyhedron has 12 edges and 6 faces, find the number of vertices.\",\n                    \"text\": \"A polyhedron has 12 edges and 6 faces, find the number of vertices.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Euler\u2019s formula is $$\\\\text{V} \\\\;\u2212\\\\; \\\\text{E} + \\\\text{F} = 2$$<br>\r\n$$\\\\text{V} \\\\;\u2013\\\\; 12 + 6 = 2 ; \\\\text{V} = 8$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following 3D shape has:<br>Faces: 5<br>Edges: 9<br>Vertices: 6\",\n                    \"text\": \"Which of the following 3D shape has:<br>Faces: 5<br>Edges: 9<br>Vertices: 6\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Cube\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Tetrahedron\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangular pyramid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Triangular prism\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A triangular prism has 5 faces, 9 edges, and 6 vertices.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which among these below is Euler's formula?\",\n                    \"text\": \"Which among these below is Euler's formula?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{F} + \\\\text{E} \\\\;-\\\\; \\\\text{V} = 2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{F} + \\\\text{E} \\\\;-\\\\; \\\\text{V} = 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"There are always relationships between faces, vertices, and edges. This relationship is explained by the formula, $$\\\\text{F} + \\\\text{V} \\\\;-\\\\; \\\\text{E} = 2$$ (Here, $$\\\\text{F} =$$ faces, $$\\\\text{V} =$$ vertices, $$\\\\text{E} =$$ edges)\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What type of faces does a cone have?\",\n                    \"text\": \"What type of faces does a cone have?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 curved faces\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 flat circle faces\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 triangle face and 1 circle face\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1 curved and 1 circular face\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A cone has 2 faces: one curved face and another flat circle face.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many edges does a cone have?\",\n                    \"text\": \"How many edges does a cone have?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A cone has only one curved edge.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has only one curved edge.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has only one curved edge.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone has only one curved edge.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A cone has only one curved edge.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A cone has only one curved edge.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following solids has the least number of faces?\",\n                    \"text\": \"Which of the following solids has the least number of faces?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Square pyramid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Rectangular pyramid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Triangular pyramid\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Triangular pyramids have only 4 faces, whereas other pyramids have 5 faces.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the number of faces of a cube is 6 and vertices is 8, find out the number of edges according to Euler's formula.\",\n                    \"text\": \"If the number of faces of a cube is 6 and vertices is 8, find out the number of edges according to Euler's formula.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to Euler\u2019s Formula, $$\\\\text{F} + \\\\text{V} = \\\\text{E} + 2$$<br>\r\n$$6 + 8 = \\\\text{E} + 2$$<br>\r\n$$14 = \\\\text{E} + 2$$<br>\r\n$$14 \\\\;\u2013\\\\; 2 = \\\\text{E}$$<br>\r\n$$\\\\text{E} = 12$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following solid shapes do not have any edges?\",\n                    \"text\": \"Which of the following solid shapes do not have any edges?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Cube\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangular prism\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangular Pyramid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Sphere\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A cube has 12 edges, a prism has 9 edges, and a pyramid has 6 edges, but a sphere does not have any edge since it is one plain round ball-like shape.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following shapes have a curved edge?\",\n                    \"text\": \"Which of the following shapes have a curved edge?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Cube\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangular prism\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangular pyramid\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Cone\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A cone is the only shape out of the given options with a curved edge in the shape of a circle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What do we call a point where two or more edges meet?\",\n                    \"text\": \"What do we call a point where two or more edges meet?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Edge\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Face\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Vertex\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A point where two edges meet in a given shape is a Vertex. A face is a side of a shape, and an edge is a line segment that joins one vertex to another.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the edges of a triangle are 12 in, 14 in, and 12 in, what will be its perimeter?\",\n                    \"text\": \"If the edges of a triangle are 12 in, 14 in, and 12 in, what will be its perimeter?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"48 in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"35 in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"65 in\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"38 in\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The perimeter of a two-dimensional shape is the sum of all the edges.<br>\r\nPerimeter $$= 12 + 14 + 12$$<br>\r\nPerimeter $$= 38$$ in\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"36-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>How many vertices does an octahedron have?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"244\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq.png\" alt=\"Vertices of an octahedron\" class=\"wp-image-24599\" title=\"Vertices of an octahedron\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq.png 247w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq-120x120.png 120w\" sizes=\"auto, (max-width: 247px) 100vw, 247px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An octahedron is a shape that is formed by joining two square pyramids at their bases. It has 6 vertices.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>Is Euler\u2019s formula true for shapes with curved surfaces?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No, Euler\u2019s formula only stands true for polyhedrons. For example, a cylinder is not a polyhedron, so the Euler\u2019s formula does not stand true for the cylinder. Let\u2019s understand how with the given figure.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"239\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq-2.png\" alt=\"Vertices of a cylinder\" class=\"wp-image-24600\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq-2.png 333w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/vertices-faq-2-300x215.png 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A cylinder has 0 vertices, 2 edges, and 3 faces.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Euler\u2019s formula: <\/strong>$\\text{V} \\;\u2212\\; \\text{E} + \\text{F} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$0 \\;\u2013\\; 2 + 3 \\neq 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1 \\neq 2$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>Is Euler\u2019s rule satisfied for a sphere?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of vertices of a sphere is zero.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of edges of a sphere is zero.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of faces of a sphere is one.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Euler\u2019s formula is <\/strong>$\\text{V} \\;\u2212\\; \\text{E} + \\text{F} = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$0 \\;-\\; 0 + 1 \\neq 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$1 \\neq 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Euler\u2019s rule is not satisfied for a sphere as it is not a polyhedron.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>Are the number of vertices equal to the number of sides for all two-dimensional shapes?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The number of vertices is equal to the number of sides only for two-dimensional polygons like triangles, squares, pentagons etc. They are not equal for two-dimensional shapes like circle and oval as they are not polygons.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>What is the difference between a vertex and an angle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Both, a vertex and an angle are formed when two rays or line segments meet. An angle is the measure of the inclination of the two rays whereas the vertex is the point of intersection of the two rays.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>Which solid space has no edges?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Spheres have no edges as they have only one curved face.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-6-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>What are polyhedrons?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-6-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Polyhedrons are three-dimensional solids that have flat polygonal faces, sharp vertices, and straight edges. Some examples of solid shapes that are polyhedrons are pyramids, cubes, and prisms.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-7-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>What does Euler\u2019s formula define?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-7-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Euler&#8217;s formula shows the relationship between faces, edges, and vertices of polyhedrons. According to the formula, the number of faces + the number of vertices $\u2013$ the number of edges $= 2$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-8-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>What is the difference between 2D and 3D shapes?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-8-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Three-dimensional shapes have three dimensions: length, breadth, height.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Two-dimensional shapes only have a breadth and length.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Some examples of 3D shapes are spheres, pyramids, cuboids, and prisms, whereas 2D shapes are squares, triangles, circles, etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-9-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>How do a vertex, edge, and face look different from each other?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-9-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A vertex is a corner, an edge is a straight line, and a face is a surface.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-10-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>What is the Euler theorem?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-10-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The Euler theorem is among the most important mathematical theorems. According to the theorem, for polyhedrons, the number of faces plus the number of vertices minus the number of edges is equal to 2.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-11-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>How are a cube and cuboid similar in terms of the number of edges?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-11-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Both cubes and cuboids are a type of prism and have 12 edges each.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-12-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>Do all shapes have only straight lines for edges?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-12-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">No, all shapes don&#8217;t need to have straight lines for edges. Shapes like a hemisphere can have a curved edge.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-13-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\"><strong>How many faces does a 2D shape have?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-13-3f840b8e-6b6a-4697-b5c1-a9561a3f677c\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Any two-dimensional shape has only one face bounded by its sides.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Vertices, Faces, Edges? Every geometric shape is composed of different parts such as vertices, faces, edges. We come across different objects with rectangular faces, circular faces, cubic faces, diamond faces, triangular faces, etc. We also know many objects that have sharp corners and edges. We will learn about vertices, faces, edges of different &#8230; <a title=\"Vertices, Faces And Edges\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/vertices-faces-edges\" aria-label=\"More on Vertices, Faces And Edges\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-24595","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/24595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=24595"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/24595\/revisions"}],"predecessor-version":[{"id":24726,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/24595\/revisions\/24726"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=24595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=24595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=24595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}