The symmetry analysis from a polytype symbol

The two meso-octahedral MDO polytypes derived in the previous section is now used to demonstrate a reverse procedure to read-out the local and global symmetry from the descriptive symbol. The permanent use of Table 5a (or Table 5b, if Z symbols are to be analyzed) is not emphasized at every step. Before starting such a task, we must check the formal correctness of a symbol the parity of any displacement character must be opposite to that of the two orientational characters above it which, in turn, must have the same parity. Also the rule T2y + T2y+i = V2/,2y+i must be observed. Otherwise, the symbol is wrong. 

Let us take an extended (more than one identity period) string of characters corresponding to the 3Tpolytype, which has six packets within the identity period  

T-operations. Evidently, 02[3 ] is the only global non-trivial x-operation because it converts any packet p or q into p+2 or q+2. In addition, there is a trivial oe -operation a translation by the identity period (and its multiples, of course). The global 04[3 ] is a consequence. Other x-operations are only local. The three packet pairs °3°, nd Y have [...(.).. /w], m. ] and m. . ] respectively as local operations 

The inversions valid for each packet pair p2j q2y+i are only local operations. If a string of characters corresponds to a centrosymmetric polytype, then this string, starting and ending with the same character(s), read forwards and backwards, must remain the same. This is not the case in polytype 3T. 

Let us now consider the meso-octahedral MDO polytype 7Mi derived above, already in the standard orientation. The only non-trivial i-operation here is the glide 

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