# Cylindrical system

### From Online Dictionary of Crystallography

Système cylindrique (Fr) Sistema cylindrico (It).

## Definition

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 Schönfliess 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.

## 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.).