Spherical system

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Système sphérique (Fr). Sistema sferico (It).


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 Schönflies symbol Order of the groupGeneral form
 \infty A_\infty 2\infty K  \infty sphere filled with
an optically active liquid
 \infty {A_\infty \over M}C  m {\bar \infty}, {2\over m}{\bar \infty} Kh  \infty stationary sphere


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

See also

  • Curie laws
  • Cylindrical system
  • Chapter of International Tables for Crystallography, Volume A, 6th edition
  • Chapter 1.1.4 of International Tables for Crystallography, Volume D