|
Conway polyhedron notation is used to describe polyhedra based on a seed polyhedron modified by various operations. The seed polyhedra are the Platonic solids, represented by the first letter of their name (T,O,C,I,D); the prisms (P''n''), antiprisms (A''n'') and pyramids (Y''n''). Any convex polyhedron can serve as a seed, as long as the operations can be executed on it. John Conway extended the idea of using operators, like truncation defined by Kepler, to build related polyhedra of the same symmetry. His descriptive operators can generate all the Archimedean solids and Catalan solids from regular seeds. Applied in a series, these operators allow many higher order polyhedra to be generated. == Operations on polyhedra == Elements are given from the seed (''v'',''e'',''f'') to the new forms, assuming seed is a convex polyhedron: (a topological sphere, Euler characteristic = 2) An example image is given for each operation, based on a cubic seed. The basic operations are sufficient to generate the reflective uniform polyhedra and theirs duals. Some basic operations can be made as composites of others. These extended operators can't be created in general from the basic operations above. The gyro/snub operations are needed to generate the uniform polyhedra and duals with rotational symmetry. Note: * - The half operator, ''h'', reduces square faces into digons, with two coinciding edges, which can be replaced by a single edge. Otherwise digons have a topological existence which can be subsequently truncated back into square faces. Special forms : The kis operator has a variation, k''n'', which only adds pyramids to ''n''-sided faces. : The truncate operator has a variation, t''n'', which only truncates order-''n'' vertices. The operators are applied like functions from right to left. For example: * the dual of a tetrahedron is ''dT''; * the truncation of a cube is ''t3C'' or ''tC''; * the truncation of a cuboctahedron is ''t4aC'' or ''taC''. All operations are ''symmetry-preserving'' except twisting ones like s and g which lose reflection symmetry. 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「Conway polyhedron notation」の詳細全文を読む スポンサード リンク
|