|
In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere. == History on four-dimensional groups == * 1889 Édouard Goursat, ''Sur les substitutions orthogonales et les divisions régulières de l'espace'', Annales scientifiques de l'École Normale Supérieure, Sér. 3, 6, (pp. 9–102, pp. 80–81 tetrahedra), Goursat tetrahedron * 1951, A. C. Hurley, ''Finite rotation groups and crystal classes in four dimensions'', Proceedings of the Cambridge Philosophical Society, vol. 47, issue 04, p. 650〔http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2039540〕 * 1962 A. L. MacKay ''Bravais Lattices in Four-dimensional Space''〔http://met.iisc.ernet.in/~lord/webfiles/Alan/CV25.pdf〕 * 1964 Patrick du Val, ''Homographies, quaternions and rotations'', quaternion-based 4D point groups * 1975 Jan Mozrzymas, Andrzej Solecki, ''R4 point groups'', Reports on Mathematical Physics, Volume 7, Issue 3, p. 363-394 * 1978 H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, ''Crystallographic Groups of Four-Dimensional Space.''〔http://journals.iucr.org/a/issues/2002/03/00/au0290/au0290.pdf〕 * 1982 N. P. Warner, ''The symmetry groups of the regular tessellations of S2 and S3'' 〔http://www.jstor.org/discover/10.2307/2397289?uid=3739736〕 * 1985 E. J. W. Whittaker, ''An atlas of hyperstereograms of the four-dimensional crystal classes'' * 1985 H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', Coxeter notation for 4D point groups * 2003 John Conway and Smith, ''On Quaternions and Octonions'', Completed quaternion-based 4D point groups * 2015 N. W. Johnson ''Geometries and Transformations'', Extended Coxeter notation for 4D point groups 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「Point groups in four dimensions」の詳細全文を読む スポンサード リンク
|