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Regular icosahedron
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<p>The regular icosahedron (or simply <i>icosahedron</i>) is a <a href="/facts/Convex_polyhedron/2pRHcRgC">convex polyhedron</a> that can be constructed from <a href="/facts/Pentagonal_antiprism/gR8aMBKN">pentagonal antiprism</a> by attaching two <a href="/facts/Pentagonal_pyramid/tN5CBPjK">pentagonal pyramids</a> with <a href="/facts/Regular_polygon/ws89Nhpt">regular faces</a> to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 <a href="/facts/Equilateral_triangle/MJomsYDS">equilateral triangles</a> as its faces, 30 edges, and 12 vertices. It is an example of a <a href="/facts/Platonic_solid/jraREXFD">Platonic solid</a> and of a <a href="/facts/Deltahedron/qDjkasx9">deltahedron</a>. The icosahedral graph represents the <a href="/facts/Skeleton_(topology)/EAt2F7tC">skeleton</a> of a regular icosahedron. </p><p>Many polyhedra are constructed from the regular icosahedron. A notable example is the <a href="/facts/Stellation/T7NY6CWv">stellation</a> of regular icosahedron, which consists of 59 polyhedrons. The <a href="/facts/Great_dodecahedron/LWt3Hgg4">great dodecahedron</a>, one of the <a href="/facts/Kepler%25E2%2580%2593Poinsot_polyhedra/mzUUgBYS">Kepler–Poinsot polyhedra</a>, is constructed by either stellation or <a href="/facts/Faceting/Yte7F7bh">faceting</a>. Some of the <a href="/facts/Johnson_solid/8SR7CyNz">Johnson solids</a> can be constructed by removing the pentagonal pyramids. The regular icosahedron's <a href="/facts/Dual_polyhedron/rkIHbmAf">dual polyhedron</a> is the <a href="/facts/Regular_dodecahedron/xClYqhcp">regular dodecahedron</a>, and their relation has a historical background on the comparison mensuration. It is analogous to a four-dimensional <a href="/facts/Polytope/a76nXrL0">polytope</a>, the <a href="/facts/600-cell/tNBtDUe9">600-cell</a>. </p><p>Regular icosahedrons can be found in nature; a well-known example is the <a href="/facts/Capsid/hm7V6Ewm">capsid</a> in biology. Other applications of the regular icosahedron are the usage of its net in <a href="/facts/Cartography/8YdDAAeX">cartography</a>, and the twenty-sided dice that may have been used in ancient times but are now <a href="/facts/D20_System/hAoRFE7f">commonplace in modern</a> <a href="/facts/Tabletop_role-playing_games/3qrTpEKy">tabletop role-playing games</a>. </p>