Section 10.1.2.3. Description of crystal and point forms

The main part of each point-group table describes the general and special crystal and point forms of that point group, in a manner analogous to the positions in a space group. The general Wyckoff position is given at the top, followed downwards by the special Wyckoff positions with decreasing multiplicity. Within each Wyckoff position, the first block refers to the basic forms, the subsequent blocks list the various types of limiting form, if any.

The columns, from left to right, contain the following data (further details are to be found below in Section 10.1.2.4, Notes on crystal and point forms):

Column 1: Multiplicity of the `Wyckoff position', i.e. the number of equivalent faces and points of a crystal or point form.

Column 2: Wyckoff letter. Each general or special `Wyckoff position' is designated by a `Wyckoff letter', analogous to the Wyckoff letter of a position in a space group (cf. Section 2.2.11 ).

Column 3: Face symmetry or site symmetry, given in the form of an `oriented point-group symbol', analogous to the oriented site-symmetry symbols of space groups (cf. Section 2.2.12 ). The face symmetry is also the symmetry of etch pits, striations and other face markings. For the two-dimensional point groups, this column contains the edge symmetry, which can be either 1 or m.

Column 4: Name of crystal form. If more than one name is in common use, several are listed. The names of the limiting forms are also given. The crystal forms, their names, eigensymmetries and occurrence in the point groups are summarized in Table 10.1.2.3, which may be useful for determinative purposes, as explained in Sections 10.2.2 and 10.2.3 . There are 47 different types of crystal form. Frequently, 48 are quoted because `sphenoid' and `dome' are considered as two different forms. It is customary, however, to regard them as the same form, with the name `dihedron'.

Name of point form (printed in italics). There exists no general convention on the names of the point forms. Here, only one name is given, which does not always agree with that of other authors. The names of the point forms are also contained in Table 10.1.2.3. Note that the same point form, `line segment', corresponds to both sphenoid and dome. The letter in parentheses after each name of a point form is explained below.

Column 5: Miller indices (hkl) for the symmetrically equivalent faces (edges) of a crystal form. In the trigonal and hexagonal crystal systems, when referring to hexagonal axes, Bravais–Miller indices (hkil) are used, with .

Coordinates x, y, z for the symmetrically equivalent points of a point form are not listed explicitly because they can be obtained from data in this volume as follows: after the name of the point form, a letter is given in parentheses. This is the Wyckoff letter of the corresponding position in the symmorphic P space group that belongs to the point group under consideration. The coordinate triplets of this (general or special) position apply to the point form of the point group.

The triplets of Miller indices (hkl) and point coordinates x, y, z are arranged in such a way as to show analogous sequences; they are both based on the same set of generators, as described in Sections 2.2.10 and 8.3.5 . For all point groups, except those referred to a hexagonal coordinate system, the correspondence between the (hkl) and the x, y, z triplets is immediately obvious.⁸

The sets of symmetrically equivalent crystal faces also represent the sets of equivalent reciprocal-lattice points, as well as the sets of equivalent X-ray (neutron) reflections.