International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2015 
International Tables for Crystallography (2015). Vol. A, ch. 1.5, pp. 8890

In the spacegroup tables of this volume, the monoclinic space group (14) is described in six different settings: for each of the `unique axis b' and `unique axis c' settings there are three descriptions specified by different cell choices (cf. Section 2.1.3.15 ). The different settings are identified by the appropriate full Hermann–Mauguin symbols. The basis transformations between the different settings are completely specified by the linear part of the transformation, the 3 × 3 matrix P [cf. equation (1.5.1.4)], as all settings of refer to the same origin, i.e. . The transformation matrices P necessary for switching between the different descriptions of can either be read off directly or constructed from the transformationmatrix data listed in Table 1.5.1.1.
(A) Transformation from (unique axis b, cell choice 1) to (unique axis c, cell choice 1). The change of the direction of the screw axis indicates that the unique direction b transforms to the unique direction c, while the glide vector along c transforms to a glide vector along a. These changes are reflected in the transformation matrix P between the basis of and of , which can be read directly from Table 1.5.1.1:

(B) Transformation from (unique axis c, cell choice 3) to (unique axis b, cell choice 1): = . A transformation matrix from directly to is not found in Table 1.5.1.1, but it can be constructed in two steps from transformation matrices that are listed there. For example:
Step 1. Unique axis c fixed: transformation from `cell choice 3' to `cell choice 1':