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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Uniform 6-polytope ： ウィキペディア英語版 Uniform 6-polytope In six-dimensional geometry, a uniform polypeton〔A proposed name polypeton (plural: polypeta) has been advocated, from the Greek root ''poly-'' meaning "many", a shortened ''penta-'' meaning "five", and suffix ''-on''. "Five" refers to the dimension of the 5-polytope facets.〕〔(Ditela, polytopes and dyads )〕 (or uniform 6-polytope) is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform polypeta has not been determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope. The simplest uniform polypeta are regular polytopes: the 6-simplex , the 6-cube (hexeract) , and the 6-orthoplex (hexacross) . == History of discovery == * Regular polytopes: (convex faces) * * 1852: Ludwig Schläfli proved in his manuscript ''Theorie der vielfachen Kontinuität'' that there are exactly 3 regular polytopes in 5 or more dimensions. * Convex semiregular polytopes: (Various definitions before Coxeter's uniform category) * * 1900: Thorold Gosset enumerated the list of nonprismatic semiregular convex polytopes with regular facets (convex regular polytera) in his publication ''On the Regular and Semi-Regular Figures in Space of n Dimensions''.〔T. Gosset: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', Messenger of Mathematics, Macmillan, 1900〕 * Convex uniform polytopes: * * 1940: The search was expanded systematically by H.S.M. Coxeter in his publication ''Regular and Semi-Regular Polytopes''. * Nonregular uniform star polytopes: (similar to the nonconvex uniform polyhedra) * * Ongoing: Thousands of nonconvex uniform polypeta are known, but mostly unpublished. The list is presumed not to be complete, and there is no estimate of how long the complete list will be, although over 10000 convex and nonconvex uniform polytera are currently known, in particular 923 with 6-simplex symmetry. Participating researchers include Jonathan Bowers, Richard Klitzing and Norman Johnson.〔(Uniform Polypeta and Other Six Dimensional Shapes )〕 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「Uniform 6-polytope」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.