{"id":155864,"date":"2022-03-26T01:07:09","date_gmt":"2022-03-25T19:37:09","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/icosahedron-meaning-structure-examples-and-faqs\/"},"modified":"2025-06-23T18:08:56","modified_gmt":"2025-06-23T12:38:56","slug":"icosahedron-meaning-structure-examples-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/","title":{"rendered":"Icosahedron &#8211; Meaning, Structure, Examples, and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Icosahedron_Meaning\" title=\"Icosahedron Meaning\">Icosahedron Meaning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#What_is_Platonic_Solid\" title=\"What is Platonic Solid?\">What is Platonic Solid?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Regular_Icosahedron\" title=\"Regular Icosahedron\">Regular Icosahedron<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Icosahedron_Structure\" title=\"Icosahedron Structure\">Icosahedron Structure<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Icosahedron_Shape_Characteristics\" title=\"Icosahedron Shape Characteristics\">Icosahedron Shape Characteristics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Surface_Area_of_Icosahedron\" title=\"Surface Area of Icosahedron\">Surface Area of Icosahedron<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Volume_of_Icosahedron\" title=\"Volume of Icosahedron\">Volume of Icosahedron<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#What_is_an_Icosahedron_Shape_Used_For\" title=\"What is an Icosahedron Shape Used For?\">What is an Icosahedron Shape Used For?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#Solved_Example\" title=\"Solved Example\">Solved Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/icosahedron\/#FAQs\" title=\"FAQs\">FAQs<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Icosahedron_Meaning\"><\/span>Icosahedron Meaning<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The icosahedron is a regular, convex polyhedron with 20 faces. It has 12 vertices and 30 edges. The faces are all triangular and the angles between adjacent faces are all 120 degrees.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155863 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/icosahedron-meaning-structure-examples-and-faqs.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/icosahedron-meaning-structure-examples-and-faqs.jpg?v=1648237026 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/icosahedron-meaning-structure-examples-and-faqs-300x212.jpg?v=1648237026 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Platonic_Solid\"><\/span>What is Platonic Solid?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A Platonic solid is a solid figure that is in the shape of a polyhedron and has faces that are all congruent regular polygons. The Platonic solids are the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron, and the icosahedron.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Regular_Icosahedron\"><\/span>Regular Icosahedron<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A regular icosahedron is a 20-sided polyhedron that has fivefold symmetry, meaning that it can be divided into five identical parts by any plane that intersects its center. Each of its faces is an equilateral triangle, and its interior is filled with 120 identical equilateral triangles.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Icosahedron_Structure\"><\/span>Icosahedron Structure<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The icosahedron is a 20-sided polyhedron. It has 12 vertices, 20 edges, and 30 faces.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Icosahedron_Shape_Characteristics\"><\/span>Icosahedron Shape Characteristics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The icosahedron is an important polyhedron because it is the shape of a soccer ball. It has 20 triangular faces, and 30 edges.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Surface_Area_of_Icosahedron\"><\/span>Surface Area of Icosahedron<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The surface area of an icosahedron is 120 \u03c0 {\\displaystyle 120\\pi } square meters.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Volume_of_Icosahedron\"><\/span>Volume of Icosahedron<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The volume of an icosahedron is (3.14) \u00d7 (5.72) \u00d7 (5.72) = 153.62 cubic units.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_an_Icosahedron_Shape_Used_For\"><\/span>What is an Icosahedron Shape Used For?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An icosahedron is a polyhedron with 20 faces. It is used in a variety of ways, including in geometry and in crystallography.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Example\"><\/span>Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A population of 200 plants is to be reduced to 100. Find the number of generations it will take.<\/p>\n<p>We can use the formula:<\/p>\n<p>N= 2N<\/p>\n<p>This will give us:<\/p>\n<p>N= 4<\/p>\n<p>So it will take 4 generations to reduce the population size by half.<\/p>\n<p dir=\"ltr\">1. What is the Volume of the Face Dice Shape Looks Like an Icosahedron With a Side Length of 5 in.<\/p>\n<p dir=\"ltr\">Solution:<\/p>\n<p dir=\"ltr\">Length of the side of the face dice shape looks like an Icosahedron =  5 in<\/p>\n<p dir=\"ltr\">Volume of Icosahedron =<\/p>\n<div class=\"MathJax_Display\">\n<p><span id=\"MathJax-Element-6-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; font-family: 'Open Sans', sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 17.3333px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;mn&gt;12&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;msup&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-101\" class=\"math\"><span id=\"MathJax-Span-102\" class=\"mrow\"><span id=\"MathJax-Span-103\" class=\"mfrac\"><span id=\"MathJax-Span-104\" class=\"mn\">5<\/span><span id=\"MathJax-Span-105\" class=\"mn\">12<\/span><\/span><span id=\"MathJax-Span-106\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-107\" class=\"mo\">(<\/span><span id=\"MathJax-Span-108\" class=\"mn\">3<\/span><span id=\"MathJax-Span-109\" class=\"mo\">+<\/span><span id=\"MathJax-Span-110\" class=\"msqrt\"><span id=\"MathJax-Span-111\" class=\"mrow\"><span id=\"MathJax-Span-112\" class=\"mn\">5<\/span><\/span>\u2013\u221a<\/span><span id=\"MathJax-Span-113\" class=\"mo\">)<\/span><span id=\"MathJax-Span-114\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-115\" class=\"msubsup\"><span id=\"MathJax-Span-116\" class=\"mi\">a<\/span><span id=\"MathJax-Span-117\" class=\"texatom\"><span id=\"MathJax-Span-118\" class=\"mrow\"><span id=\"MathJax-Span-119\" class=\"mn\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>5<\/mn><mn>12<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><msup><mi>a<\/mi><mrow class=\"MJX-TeXAtom-ORD\"><mn>3<\/mn><\/mrow><\/msup><\/math>\n<p>&nbsp;<\/p>\n<\/div>\n<p dir=\"ltr\">Volume =<\/p>\n<div class=\"MathJax_Display\">\n<p><span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; font-family: 'Open Sans', sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 17.3333px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;mn&gt;12&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;msup&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-120\" class=\"math\"><span id=\"MathJax-Span-121\" class=\"mrow\"><span id=\"MathJax-Span-122\" class=\"mfrac\"><span id=\"MathJax-Span-123\" class=\"mn\">5<\/span><span id=\"MathJax-Span-124\" class=\"mn\">12<\/span><\/span><span id=\"MathJax-Span-125\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-126\" class=\"mo\">(<\/span><span id=\"MathJax-Span-127\" class=\"mn\">3<\/span><span id=\"MathJax-Span-128\" class=\"mo\">+<\/span><span id=\"MathJax-Span-129\" class=\"msqrt\"><span id=\"MathJax-Span-130\" class=\"mrow\"><span id=\"MathJax-Span-131\" class=\"mn\">5<\/span><\/span>\u2013\u221a<\/span><span id=\"MathJax-Span-132\" class=\"mo\">)<\/span><span id=\"MathJax-Span-133\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-134\" class=\"msubsup\"><span id=\"MathJax-Span-135\" class=\"mn\">5<\/span><span id=\"MathJax-Span-136\" class=\"texatom\"><span id=\"MathJax-Span-137\" class=\"mrow\"><span id=\"MathJax-Span-138\" class=\"mn\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>5<\/mn><mn>12<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><msup><mn>5<\/mn><mrow class=\"MJX-TeXAtom-ORD\"><mn>3<\/mn><\/mrow><\/msup><\/math>\n<p>&nbsp;<\/p>\n<\/div>\n<p dir=\"ltr\">=<\/p>\n<div class=\"MathJax_Display\">\n<p><span id=\"MathJax-Element-8-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; font-family: 'Open Sans', sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 17.3333px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;625&lt;\/mn&gt;&lt;mn&gt;12&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;msup&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/msup&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-139\" class=\"math\"><span id=\"MathJax-Span-140\" class=\"mrow\"><span id=\"MathJax-Span-141\" class=\"mfrac\"><span id=\"MathJax-Span-142\" class=\"mn\">625<\/span><span id=\"MathJax-Span-143\" class=\"mn\">12<\/span><\/span><span id=\"MathJax-Span-144\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-145\" class=\"mo\">(<\/span><span id=\"MathJax-Span-146\" class=\"mn\">3<\/span><span id=\"MathJax-Span-147\" class=\"mo\">+<\/span><span id=\"MathJax-Span-148\" class=\"msqrt\"><span id=\"MathJax-Span-149\" class=\"mrow\"><span id=\"MathJax-Span-150\" class=\"mn\">5<\/span><\/span>\u2013\u221a<\/span><span id=\"MathJax-Span-151\" class=\"mo\">)<\/span><span id=\"MathJax-Span-152\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-153\" class=\"msubsup\"><span id=\"MathJax-Span-154\" class=\"mn\">5<\/span><span id=\"MathJax-Span-155\" class=\"texatom\"><span id=\"MathJax-Span-156\" class=\"mrow\"><span id=\"MathJax-Span-157\" class=\"mn\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>625<\/mn><mn>12<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><msup><mn>5<\/mn><mrow class=\"MJX-TeXAtom-ORD\"><mn>3<\/mn><\/mrow><\/msup><\/math>\n<p>&nbsp;<\/p>\n<\/div>\n<p dir=\"ltr\">=<\/p>\n<div class=\"MathJax_Display\">\n<p><span id=\"MathJax-Element-9-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; font-family: 'Open Sans', sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 17.3333px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mn&gt;625&lt;\/mn&gt;&lt;mn&gt;12&lt;\/mn&gt;&lt;\/mfrac&gt;&lt;mo&gt;&amp;#x00D7;&lt;\/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;msqrt&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/msqrt&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-158\" class=\"math\"><span id=\"MathJax-Span-159\" class=\"mrow\"><span id=\"MathJax-Span-160\" class=\"mfrac\"><span id=\"MathJax-Span-161\" class=\"mn\">625<\/span><span id=\"MathJax-Span-162\" class=\"mn\">12<\/span><\/span><span id=\"MathJax-Span-163\" class=\"mo\">\u00d7<\/span><span id=\"MathJax-Span-164\" class=\"mo\">(<\/span><span id=\"MathJax-Span-165\" class=\"mn\">3<\/span><span id=\"MathJax-Span-166\" class=\"mo\">+<\/span><span id=\"MathJax-Span-167\" class=\"msqrt\"><span id=\"MathJax-Span-168\" class=\"mrow\"><span id=\"MathJax-Span-169\" class=\"mn\">5<\/span><\/span>\u2013\u221a<\/span><span id=\"MathJax-Span-170\" class=\"mo\">)<\/span><\/span><\/span><\/span><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>625<\/mn><mn>12<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><\/math>\n<p>&nbsp;<\/p>\n<\/div>\n<p dir=\"ltr\">= 272,71 cm<sup>3<\/sup><\/p>\n<p dir=\"ltr\">Therefore, the volume of the icosahedron is 272,71 cm<sup>3<\/sup>.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. What is an icosahedron?<br \/>\nA: An icosahedron is a polyhedron with 20 faces, each of which is an equilateral triangle.<\/p>\n<p>2. How many vertices does an icosahedron have?<br \/>\nA: An icosahedron has 12 vertices.<\/p>\n<p>3. How many edges does an icosahedron have?<br \/>\nA: An icosahedron has 30 edges.<\/p>\n<p>4. What is the dual of an icosahedron?<br \/>\nA: The dual of an icosahedron is a dodecahedron.<\/p>\n<p>5. What is the angle between two adjacent faces of an icosahedron?<br \/>\nA: The angle between two adjacent faces of an icosahedron is 138.19 degrees.<\/p>\n<p>6. What is the surface area of an icosahedron with edge length &#8220;a&#8221;?<br \/>\nA: The surface area of an icosahedron with edge length &#8220;a&#8221; is 5\u221a3a\u00b2.<\/p>\n<p>7. What is the volume of an icosahedron with edge length &#8220;a&#8221;?<br \/>\nA: The volume of an icosahedron with edge length &#8220;a&#8221; is (5\/12)(3+\u221a5)a\u00b3.<\/p>\n<p>8. What is the symmetry group of an icosahedron?<br \/>\nA: The symmetry group of an icosahedron is the group of all rotations and reflections that leave the icosahedron invariant. This group is known as the icosahedral symmetry group or Icosahedral group and denoted by I or Y.<\/p>\n<p>9. What are some real-life examples of an icosahedron?<br \/>\nA: Examples of icosahedral shapes can be found in viruses, geodesic domes, soccer balls, and fullerene molecules.<\/p>\n<p>10. Who discovered the icosahedron?<br \/>\nA: The icosahedron has been known since ancient times and its discovery is not attributed to any one person.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Icosahedron Meaning The icosahedron is a regular, convex polyhedron with 20 faces. It has 12 vertices and 30 edges. 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