Cylindrical system

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Système cylindrique (Fr). Zylindrisches System (Ge). Sistema cilindrico (It). Sistema cilíndrico (Sp).


The cylindrical system contains non-crystallographic point groups with one axis of revolution (or isotropy axis). There are five groups in the spherical system:

Hermann-Mauguin symbol Short Hermann-Mauguin symbol Schönflies symbol Order of the groupGeneral form
 A_\infty \infty C_\infty  \infty rotating cone
 {A_\infty \over M}C  {\bar \infty} C_{\infty h} \equiv S_{\infty} \equiv C_{\infty i}  \infty rotating finite cylinder
 A_\infty \infty A_2  \infty 2 D_{\infty }  \infty finite cylinder
submitted to equal and
opposite torques
 A_\infty M \infty m C_{\infty v}  \infty stationary cone
 {A_\infty \over M} {\infty A_2 \over \infty M} C  {\bar \infty}m \equiv {\bar \infty} {2\over m} D_{\infty h} \equiv D_{\infty d}  \infty stationary finite cylinder


Note that  A_\infty M represents the symmetry of a force, or of an electric field, and that  {A_\infty \over M}C represents the symmetry of a magnetic field (Curie, 1894), while  {A_\infty \over M} {\infty A_2 \over \infty M} C represents the symmetry of a uniaxial compression.


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