# Cylindrical system

### From Online Dictionary of Crystallography

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

## 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 | Schönflies symbol | Order of the group | General form |
---|---|---|---|---|

rotating cone | ||||

rotating finite cylinder | ||||

finite cylinder submitted to equal and opposite torques |
||||

stationary cone | ||||

stationary finite cylinder |

Note that represents the symmetry of a force, or of an electric field, and that represents the symmetry of a magnetic field (Curie, 1894), while 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). *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 3.2.1.4 of
*International Tables for Crystallography, Volume A*, 6th edition - Chapter 1.1.4 of
*International Tables for Crystallography, Volume D*