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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 Binary octahedral group ： ウィキペディア英語版 Binary octahedral group In mathematics, the binary octahedral group, name as 2O or <2,3,4> is a certain nonabelian group of order 48. It is an extension of the octahedral group ''O'' or (2,3,4) of order 24 by a cyclic group of order 2, and is the preimage of the octahedral group under the 2:1 covering homomorphism $\backslash operatorname(3)\; \backslash to\; \backslash operatorname(3)$ of the special orthogonal group by the spin group. It follows that the binary octahedral group is a discrete subgroup of Spin(3) of order 48. The binary octahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism $\backslash operatorname(3)\; \backslash cong\; \backslash operatorname(1)$ where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.) ==Elements== Explicitly, the binary octahedral group is given as the union of the 24 Hurwitz units :$\backslash (\backslash pm\; 1\; \backslash pm\; i\; \backslash pm\; j\; \backslash pm\; k)\backslash \}$ with all 24 quaternions obtained from :$\backslash tfrac(\backslash pm\; 1\; \backslash pm\; 1i\; +\; 0j\; +\; 0k)$ by a permutation of coordinates (all possible sign combinations). All 48 elements have absolute value 1 and therefore lie in the unit quaternion group Sp(1). 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「Binary octahedral group」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.