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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 5-polytope ： ウィキペディア英語版 Uniform 5-polytope In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets. The complete set of convex uniform 5-polytopes 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 diagrams. == 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 polychora) 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: * * 1940-1988: The search was expanded systematically by H.S.M. Coxeter in his publication ''Regular and Semi-Regular Polytopes I, II, and III''. * * 1966: Norman W. Johnson completed his Ph.D. Dissertation under Coxeter, ''The Theory of Uniform Polytopes and Honeycombs'', University of Toronto 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 5-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.