# Crystalline System

A crystalline system is a classification of the crystals on the basis of their characteristic of Symétrie, knowing that the priority given to certain criteria rather than to others leads to various systems.

The Symétrie of the conventional mesh makes it possible to classify the crystals into different crystalline families : four in two-dimensional space, six in three-dimensional space.

A finer classification gathers the crystals into different systems . There exist two types of systems , according to whether the criterion of classification is the symmetry of the network or morphological symmetry . Historically, these two systems were indistinctly called crystalline system , which was at the origin of confusion in the mineralogical literature especially .

## Reticular classification: reticular systems

When one classifies the crystals on the basis of symmetry of their network, one obtains a whole of four (two-dimensional space) or seven (three-dimensional space) systems which in the old French-speaking mineralogical literature (see especially the works of Georges Friedel) were called crystalline systems . The official term chosen by the International union of crystallography is reticular systems ( lattice systems in English).

A reticular system gathers any crystal having jointly the specific group network. The following tables summarize the reticular systems.

## Trigonal versus rhomboedric

In the French-speaking mineralogical medium, the two adjectives, trigonal and rhomboedric , are often regarded as equivalents. However the trigonal term qualifies any crystal having like rotational symmetry of a maximum nature a rotation of ±120º around one only axis, independently of the type of network (hexagonal or rhomboedric): it thus characterizes a crystalline system and not a network. On the other hand, the term rhomboedric qualifies any crystal having a network of symmetry $\ bar \left\{3\right\}$ m : it characterizes this time a reticular system and not a crystalline system. The cause of this confusion in the mineralogical literature is that originally the two types of system were described as " cristallin".

## Morphological classification: crystalline systems

The classification of the crystals on the basis of their morphological symmetry, as well as symmetry of their physical properties, was introduced by the German crystallographers under the name of crystalline system , which was retained like official name by the International union of crystallography.

A crystalline system gathers any crystal characterized by the presence of minimal elements of symmetry, to which can be possibly added others until obtaining of them the symmetry of a network. A crystal which has the full symmetry of its network is known as holohedron ; a crystal whose symmetry is lower than that of its network is known as mérièdre . The following tables summarize the crystalline systems, where “An” means point (in two dimensions) or an axis (in three dimensions) of rotation of 2π /n and “ m ” indicate a line (in two dimensions) or plan (in three dimensions) of reflection (mirror).

## Correspondence between systems and networks of Faced in three-dimensional space

The 14 networks of Faced are defined starting from the conventional mesh of the network. In three-dimensional space, there exist 7 primitive solids, which carry same designations as the 7 reticular systems: triclinic, monoclinical, orthorhombic, quadratic, rhomboedric, hexagonal, cubic.

The correspondence is on the other hand only partial in the case of the crystalline systems. The crystals of the trigonal system can have a network either hexagonal or rhomboedric. On the 29 groups of space which the 5 count trigonal classes, only 7 of them have an elementary mesh rhomboedric (they are the groups indicated by the letter R ); the 22 other groups of space have an elementary mesh hexagonal ( P ). As the conventional mesh ''' ''' of the network rhomboedric is hexagonal, one often uses a hexagonal reference frame to describe the atomic positions of a crystal pertaining to the reticular system rhomboedric. For the 6 other cases, the correspondence between crystalline systems and systems reticular are complete.

The following table show the correspondences between crystalline families, networks of Faced, reticular systems and crystalline systems in three-dimensional space.

## 230 types of groups of space

Note . The plan of the type E is a plan with double slip, along two different directions, which exists in five types of groups of space to centered network. The use of the symbol E became official as from the fifth edition of volume has international Tables of crystallography (2002).

## Terms used in crystallography

• a diplohedron is a combination of two rhombohedrons.
• ditétragonale qualifies a form built on a basis at 8 sides.
• ditrigonale qualifies a form built on a basis at 6 sides.
• a dodecahedron is a crystal with twelve faces; the faces are pentagon S in the case of a regular Dodécaèdre.
• énantiomorphe qualifies a crystal which comprises paired elements of the same form, but symmetrically reversed.
• the holohedrism is the property of a crystal whose symmetry is exactly that of the periodic network which corresponds to him.
• the mériédrie is the property of a crystal whose symmetry is lower than that of the periodic network which corresponds to him. It is divided into:
• hemihedrism , or mériédrie of a nature 2
• tetartohedrism , or mériédrie of a nature 4
• ogdoédrie , or mériédrie of a nature 8
• holoaxial qualifies a crystal which has all its axes of symmetry.
• a pinacoidal is a “open” form delimited by 2 parallel faces.
• a rhombohedron is a parallelepiped whose faces are rhombuses.
• a scalénoèdre is an irregular polyhedron with scalene faces, i.e. which form triangles whose three sides are unequal.
• a sphénoèdre is a polyhedron with acute faces crossing two to two in corners.
• tétragonale qualifies a form built on a basis at 4 sides.
• a trapezohedron is a solid whose faces are trapezoids.
• trigonal qualifies a form built on a basis at 3 sides.