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icosahedron <pl icosahedrons, icosahedra> [Brit ˌʌɪkɒsəˈhiːdrən, Am aɪˌkoʊsəˈhidrən] N

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This polyhedron looks very similar to the uniform truncated icosahedron which has 12 pentagons, but only 20 hexagons. en.wikipedia.org

Conversely, supposing the existence of a regular icosahedron, lines defined by its six pairs of opposite vertices form an equiangular system. en.wikipedia.org

Unlike the great icosahedron and great dodecahedron, the great icosidodecahedron is not a stellation of the icosidodecahedron. en.wikipedia.org

This is the case for the icosahedron, great icosahedron, small snub icosicosidodecahedron, and small retrosnub icosicosidodecahedron. en.wikipedia.org

It can also be called an "expanded" or "cantellated" dodecahedron or icosahedron, from truncation operations on either uniform polyhedron. en.wikipedia.org

These all have icosahedral symmetry and may be obtained as stellations of the dodecahedron and the icosahedron. en.wikipedia.org

Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere. en.wikipedia.org

The tetrahedron, octahedron, icosahedron, and great icosahedron appear commonly in non-prismatic uniform polychora, but not in their snub constructions. en.wikipedia.org

Note the duality between cube and octahedron, and between dodecahedron and icosahedron. en.wikipedia.org

For example the cube and the regular octahedron share the same symmetry, as do the regular dodecahedron and icosahedron. en.wikipedia.org

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