600-cell

<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the 600-cell is the <a href="/facts/Convex_regular_4-polytope/lFf8IH1C">convex regular 4-polytope</a> (four-dimensional analogue of a <a href="/facts/Platonic_solid/jraREXFD">Platonic solid</a>) with <a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli symbol</a> {3,3,5}.
It is also known as the C600, hexacosichoron and hexacosihedroid.
It is also called a tetraplex (abbreviated from "tetrahedral complex") and a <a href="/facts/Polytetrahedron/tdKsUbbB">polytetrahedron</a>, being bounded by tetrahedral <a href="/facts/Cell_(geometry)/T2E6BTU4">cells</a>.
</p><p>The 600-cell's boundary is composed of 600 <a href="/facts/Tetrahedron/7mkSrl6j">tetrahedral</a> <a href="/facts/Cell_(mathematics)/T2E6BTU4">cells</a> with 20 meeting at each vertex.
Together they form 1200 triangular faces, 720 edges, and 120 vertices.
It is the 4-<a href="/facts/Four-dimensional_space/vFQd0M7T">dimensional analogue</a> of the <a href="/facts/Icosahedron/wWbpnDYp">icosahedron</a>, since it has five <a href="/facts/Tetrahedron/7mkSrl6j">tetrahedra</a> meeting at every edge, just as the icosahedron has five <a href="/facts/Triangle/cRXUwsMn">triangles</a> meeting at every vertex.
Its <a href="/facts/Dual_polytope/rkIHbmAf">dual polytope</a> is the <a href="/facts/120-cell/W4nroBjJ">120-cell</a>.
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600-cell open-in-new

600-cell