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Snub polyhedron : ウィキペディア英語版
Snub polyhedron

A snub polyhedron is a polyhedron obtained by alternating a corresponding omnitruncated polyhedron.
Chiral snub polyhedra do not have reflection symmetry and hence have two enantiomorphous forms which are reflections of each other. Their symmetry groups are all point groups and are one of:
*O - chiral octahedral symmetry; the rotation group of the cube and octahedron; order 24.
*I - chiral icosahedral symmetry; the rotation group of the icosahedron and the dodecahedron; order 60.
For example, the snub cube:
Snub polyhedra have Wythoff symbol | ''p q r'' and by extension, vertex configuration 3.''p''.3.''q''.3.''r''. Retrosnub polyhedra (a subset of the snub polyhedron, containing the great icosahedron, small retrosnub icosicosidodecahedron, and great retrosnub icosidodecahedron) still have this form of Wythoff symbol, but their vertex configurations are instead (3.''−p''.3.''−q''.3.''−r'')/2.
Among the snub polyhedra that cannot be otherwise generated, only the pentagonal antiprism, pentagrammic antiprism, pentagrammic crossed-antiprism, small snub icosicosidodecahedron and small retrosnub icosicosidodecahedron are known to occur in any non-prismatic uniform 4-polytope. The tetrahedron, octahedron, icosahedron, and great icosahedron appear commonly in non-prismatic uniform 4-polytopes, but not in their snub constructions. Every snub polyhedron however can appear in the polyhedral prism based on them.
==List of snub polyhedra==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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