The ITA settings include (i) origin choice 1 settings for centrosymmetric groups; (ii) rhombohedral-axes settings for rhombohedral groups, and (iii) 530 non-conventional settings of monoclinic and orthorhombic space groups listed in ITA:
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.
Orthorhombic groups: the ITA settings include up to six different settings corresponding to the six permutations of the basis vectors a, b or c.
Each ITA setting is specified by a transformation matrix (P,p) which relates de bases of the non-standard setting (a, b, c)n to that of the standard one (a, b, c)s