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Compound of two icosahedra : ウィキペディア英語版 | Compound of two icosahedra
|- |bgcolor=#e7dcc3|Coxeter diagrams|| |- |bgcolor=#e7dcc3|Polyhedra||2 icosahedra |- |bgcolor=#e7dcc3|Faces||16+24 triangles |- |bgcolor=#e7dcc3|Edges||60 |- |bgcolor=#e7dcc3|Vertices||24 |- |bgcolor=#e7dcc3|Symmetry group||octahedral (''Oh'') |- |bgcolor=#e7dcc3|Subgroup restricting to one constituent||pyritohedral (''Th'') |} This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry ''Oh''. As a holosnub, it is represented by Schläfli symbol β and Coxeter diagram . The triangles in this compound decompose into two orbits under action of the symmetry group: 16 of the triangles lie in coplanar pairs in octahedral planes, while the other 24 lie in unique planes. It shares the same vertex arrangement as a nonuniform truncated octahedron, having irregular hexagons alternating with long and short edges. The icosahedron, as a uniform ''snub tetrahedron'', is similar to these snub-pair compounds: compound of two snub cubes and compound of two snub dodecahedra. == Cartesian coordinates == Cartesian coordinates for the vertices of this compound are all the permutations of : (±1, 0, ±τ) where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Compound of two icosahedra」の詳細全文を読む
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