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Compound of four octahedra with rotational freedom : ウィキペディア英語版 | Compound of four octahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by an equal angle θ about a separate axis passing through the centres of two opposite octahedral faces, in such a way as to preserve pyritohedral symmetry. Superimposing this compound with a second copy, in which the octahedra have been rotated by the same angle θ in the opposite direction, yields the compound of eight octahedra with rotational freedom. When θ=0, all four octahedra coincide. When θ is 60 degrees, the more symmetric compound of four octahedra (without rotational freedom) arises. In another notable case (pictured), for a certain intermediate value of θ in which 24 of the triangles form coplanar pairs, the compound assumes the form of the compound of five octahedra with one of the octahedra removed. ==References==
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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 four octahedra with rotational freedom」の詳細全文を読む
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