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In mathematics, there are two competing definitions for a chiral polytope. One is that it is a polytope that is chiral (or "enantiomorphic"), meaning that it does not have mirror symmetry. By this definition, a polytope that lacks any symmetry at all would be an example of a chiral polytope. The other, competing definition of a chiral polytope is that it is a polytope that is as symmetric as possible without being mirror-symmetric, formalized in terms of the action of the symmetry group of the polytope on its flags. By this definition, even highly-symmetric and enantiomorphic polytopes such as the snub cube are not chiral. Indeed, much of the study of symmetric but chiral polytopes has been carried out in the framework of abstract polytopes, because of the paucity of geometric examples. ==Polytopes without mirror symmetry== Many polytopes lack mirror symmetry, and in that sense form chiral polytopes. The simplest example is a scalene triangle.〔.〕 It is possible for polytopes to have a high degree of symmetry, but yet to lack mirror symmetry; an example is the snub cube, which is vertex-transitive and chiral in this sense.〔.〕 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「Chiral polytope」の詳細全文を読む スポンサード リンク
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