The crystalline classes are categories which allow to classify the groups of space; groups which describe the Symétrie atomic structure of a Cristal.

Geometrical

A geometrical crystalline class (often shortened in crystalline class ) contains all the groups of space having same a specific group.

The geometrical crystalline class is indicated by the symbol of Hermann - Mauguin of the specific group.

There exists:

* 2 geometrical crystalline classes in unidimensional space;

* 10 in two-dimensional space;

* 32 in three-dimensional space.

Example

The groups of space of the type P 2 m , P 2₁/ m , C 2 m , P 2 C , P 2₁/ C and C 2 C belong to the geometrical crystalline class 2 m .

Arithmetic

A arithmetic crystalline class contains all the groups of space having same a specific group and same the mode of network.

The arithmetic crystalline class is indicated by the symbol of Hermann - Mauguin of the specific group followed by the symbol of the network.

There exists:

* 2 arithmetic crystalline classes in unidimensional space;

* 13 in two-dimensional space;

* 73 in three-dimensional space.

Example

The groups of space of the type P 2 m , P 2₁/ m , P 2 C and P 2₁/ C belong to the arithmetic crystalline class 2 mP , while the groups of space of the type C 2 m and C 2 C belong to the arithmetic crystalline class 2 mC .

Nomenclature of the geometrical crystalline classes

There exist two nomenclatures of the 32 geometrical crystalline classes of three-dimensional space: first is due to Georges Friedel, the second with Paul Heinrich von Groth.

• the nomenclature of Friedel is based on the relation groupe - sous-groupe which depends on the symmetry of the network. The crystals of the crystalline Système trigonal can have either a hexagonal network ( HP ), or a network rhomboedric ( hR ). For this reason, the trigonal crystalline classes take two names different in the nomenclature from Friedel.

• the nomenclature of Groth is based on the name of the form { HKL } of each specific group.

The nomenclature of Groth is used than that of Friedel.

Note on the terminology

The works of Minéralogie frequently use the " term; classify cristalline" like synonym of specific group. This practice is criticizable insofar as that encourages to confuse a category (the class), i.e. a particular species of objects, with what characterizes these objects with knowing the specific group.

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