SPACE ORIENTATION AND SYMBOL DEFINITION

Mica polytypes can belong to five symmetries A, T, O, M and A (Takeda 1971). In both the Pauling and the Trigonal models, the lattice of triclinic polytypes is metrically monoclinic, and the (001) projection of the c axis, labeled c , can take three values 0, a /3, 6 /3, on the basis of which mica polytypes are classified into orthogonal. Class a and Class b respectively. The number A of layers building a polytype can be expressed as  

Class a polytypes. Each orientation corresponds to a different c projection, i.e. to a different character of Ev, from 0 to 5 . Among these, there is only one that corresponds to the /(-unique setting with an obtuse P angle that with Ev = (0 , i.e. c  

Orthogonal polytypes. The six orientations correspond to Ev = , i.e. c = (0, 0), and they are equivalent for hexagonal, trigonal and triclinic polytypes, whereas for orthorhombic and monoclinic polytypes only two orientations, related by 180° rotation around c = c axis, lead to the correct orientation of the symmetry elements. 

Because both the reticular features and the OD character are based on the geometry of the layer stacking in polytypes, some relations between the OD and the reticular classifications can be established (Backhaus and Durovic 1984 Nespolo 1999). 

Subfamily B. These polytypes are described by orientational symbols with characters of alternating parity, i.e. by all-odd characters in the RTW symbol. Successive layers are related by (2 +l)x60° rotations. Only polytypes with an even number of layers appear in this subfamily. In addition, because layers with different orientational parity have an opposite x component of the stacking vector, Ev is ( ), (+) or -) and it is not possible to have a Class a polytype. 

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