Cylindrical system

From Online Dictionary of Crystallography

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Système cylindrique (Fr). Sistema cilindrico (It).


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
[math] A_\infty[/math] [math]\infty[/math] [math]C_\infty [/math] [math] \infty[/math] rotating cone
[math] {A_\infty \over M}C[/math] [math] {\bar \infty}[/math] [math]C_{\infty h} \equiv S_{\infty} \equiv C_{\infty i}[/math] [math] \infty[/math] rotating finite cylinder
[math] A_\infty \infty A_2[/math] [math] \infty 2[/math] [math]D_{\infty }[/math] [math] \infty[/math] finite cylinder
submitted to equal and
opposite torques
[math] A_\infty M[/math] [math]\infty m[/math] [math]C_{\infty v}[/math] [math] \infty[/math] stationary cone
[math] {A_\infty \over M} {\infty A_2 \over \infty M} C[/math] [math] {\bar \infty}m \equiv {\bar \infty} {2\over m}[/math] [math]D_{\infty h} \equiv D_{\infty d}[/math] [math] \infty[/math] stationary finite cylinder


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