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Spherical system

The spherical system contains non-crystallographic point groups with more than one axis of revolution. These groups therefore contain an infinity of axes of revolution (or isotropy axis). There are two groups in the spherical system:

Hermann-Mauguin symbol Short Hermann-Mauguin symbol Schönfliess symbol order of the group general form
\[\infty\,A_{\infty}\] \[2\infty\] K \[\infty\] sphere filled with 
an optically active liquid
\[\infty\frac{A_{\infty}}{M}C\] \[m\bar\infty,\frac{2}{m}\bar\infty\] Kh \[\infty\] stationary sphere

History

The groups containing isotropy axes were introduced by P. Curie (1859-1906) in order to describe the symmetry of physical systems (Curie P. (1884). Sur les questions d'ordre: répétitions. Bull. Soc. Fr. Minéral.7, 89-110; Curie P. (1894). Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique. J. Phys. (Paris)3, 393-415.).

See also

Section 10.1.4 of International Tables of Crystallography, Volume A
Section 1.1.4 of International Tables of Crystallography, Volume D