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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 Clebsch cubic surface ： ウィキペディア英語版 Clebsch surface In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface is a non-singular cubic surface studied by and all of whose 27 exceptional lines can be defined over the real numbers. The term Klein's icosahedral surface can refer to either this surface or its blowup at the 10 Eckardt points. ==Definition== The Clebsch surface is the set of points (''x''0:''x''1:''x''2:''x''3:''x''4) of P4 satisfying the equations :$\backslash displaystyle\; x\_0+x\_1+x\_2+x\_3+x\_4\; =\; 0$ :$\backslash displaystyle\; x\_0^3+x\_1^3+x\_2^3+x\_3^3+x\_4^3\; =\; 0.$ Eliminating ''x''0 shows that it is also isomorphic to the surface :$\backslash displaystyle\; x\_1^3+x\_2^3+x\_3^3+x\_4^3\; =\; (x\_1+x\_2+x\_3+x\_4)^3$ in P3. The symmetry group of the surface is the symmetric group ''S''5 of order 120, acting by permutations of the coordinates (in ''P''4). Up to isomorphism, the Clebsch surface is the only cubic surface with this automorphism group. 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「Clebsch surface」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.