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7 systems of crystallization:  There are 32 possibilities of combinations of the elements of symmetry (axis of 
rotation, symmetry plane, centers combined inversion and operations).  
Since the discovery of the crystals reticular structure, one could show by calculation that to these 32 classes
which relate to the shapes of the crystals, correspond 230 types of network.
One immediately realizes the complexity of the reasoning which should be made to know all the possible 
combinations.  The 32 classes are grouped in 7 systems.  Here are the figures. 
Go to Garnet Go to Zircon Go to Apatite
Diamond, garnet, spinell. Zircon Beryl, Apatite
 (Subdivision of the hexagonal system)  


Go to Corundum   Go to Tourmaline Go to Topaz      Go to Orthoclase

Calcite, corundum, tourmaline, quartz. Chrysoberyl, topaz Orthoclase
Symmetry of crystals : Go to Albite
Crystals show in their form and their appear the following symmetrical operations:  > >

· Rotation

· Inversion by symmetry plane

· Inversion by a center

· Combination of rotation and inversion

structure of the properties of characteristic
symmetry.  And like there is a cor - 
respondence between reticular plans and 
faces of the crystals, there is a 
fundamental correspondence between
internal symmetry and external symmetry.
We imagine the drawing of a tapestry, it 
will repeat ourselves by a simple parallel
displacement (translation). When a crystal is examined, the first
All the geometrical operations which  point which draws the attention is a
cause a repetition of the pattern are certain symmetry.  One can see the
called operations of symmetry.  In the repetition of faces identical to various
shape of the crystals (external format), places of the crystal. These repetitions
this translation does not appear directly. are controls by laws of symmetry,
On the other hand, in their morphology, Albite the way in which they are repeated
is determined by operators of 
symmetry, there are three principal
types of them:  Axis of symmetry,
symmetry plane and the center
of symmetry.
 ¦Gemology ¦ Corundums ¦ Tourmaline Characteristics ¦ Garnets ¦ Cutting Styles ¦
All of the pictures on this website have been shot by
Text written by Alain Darbellay.
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