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In geometry, an alternation or ''partial truncation'', is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.〔Coxeter, Regular polytopes, pp. 154–156 8.6 Partial truncation, or alternation〕 Coxeter labels an ''alternation'' by a prefixed by an h, standing for ''hemi'' or ''half''. Because alternation reduce all polygon faces to half as many sides, it can only be applied for polytopes with all even-sided faces. An alternated square face becomes a digon, and being degenerate, is usually reduced to a single edge. More generally any vertex-uniform polyhedron or tiling with a vertex configuration consisting of all even-numbered elements can be ''alternated''. For example the alternation a vertex figure with ''2a.2b.2c'' is ''a.3.b.3.c.3'' where the three is the number of elements in this vertex figure. A special case is square faces whose order divide in half into degenerate digons. So for example, the cube ''4.4.4'' is alternated as ''2.3.2.3.2.3'' which is reduced to 3.3.3, being the tetrahedron, and all the 6 edges of the tetrahedra can also be seen as the degenerate faces of the original cube. == Snub == A snub can be seen as an alternation of a truncated regular or truncated quasiregular polyhedron. In general a polyhedron can be snubbed if its truncation has only even-sided faces. All truncated rectified polyhedra can be snubbed, not just from regular polyhedra. The snub square antiprism is an example of a general snub, and can be represented by ss, with the square antiprism, s. 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「Alternation (geometry)」の詳細全文を読む スポンサード リンク
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