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ITA Settings of Space Groups

The option 'ITA Settings' gives access to the conventional settings and choices of the unit cells for all space groups. Accessible are also all various settings of monoclinic and orthorhombic space groups as listed in Table of Volume A of International Tables for Crystallography (2016, referred to as ITA). In the case of monoclinic groups, the ITA settings refer to different choices of the unique axis (along the basis vectors a, b or c) combined with different choices for the oblique axes (described as cell choices 1, 2 or 3 in ITA). There could be up to 18 different settings for a monoclinic group. Following Table of ITA, for each of the monoclinic space groups No. 5, 7, 8, 9, 10, 12, 13, 14 and 15, 18 different cases are distinguished, each case specified by the choice of the monoclinic axis, the cell choice and a transformation matrix (P,p) that relates the non-standard basis (a,b,c)n to the standard one (a,b,c)s:

(a,b,c)n = (a,b,c)sP,    On = p + Os
For the rest of monoclinic space groups (Nos. 3, 4, 6, 10 and 11), the option ITA settings gives access only to three different settings (corresponding to the choice of the monoclinic axis), each specified by a transformation matrix. For alternative transformation matrices, cf. Table of ITA (2016).

The option ITA settings for the orthorhombic groups include up to six different settings corresponding to the six permutations of the basis vectors a, b or c.

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