Spherical system

Système sphérique (Fr).

Definition

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
[math] \infty A_\infty[/math]	[math]2\infty[/math]	K	[math] \infty[/math]	sphere filled with an optically active liquid
[math] \infty {A_\infty \over M}C[/math]	[math] m {\bar \infty}[/math], [math]{2\over m}{\bar \infty} [/math]	Kh	[math] \infty[/math]	stationary sphere

History

The groups containing isotropy axes were introduced by P. Curie in order to describe the symmetry of physical systems (Curie P. (1884). Sur les questions d'ordre: rép\étitions. 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.).