Form

Forme (Fr), Forma (It), 結晶形 (Ja)

For a point group P a form is a set of all symmetrically equivalent "elements", namely:

• in vector space, a crystal form or face form is a set of all symmetrically equivalent faces;
• in point space, a point form is a set of all symmetrically equivalent points.

The polyhedron or polygon of a point form is dual to the polyhedron of the corresponding face form, where "dual" means that they have the same number of edges but the number of faces and vertices is interchanged.

Forms in point groups correspond to crystallographic orbits in space groups.

Classification of forms

Forms are classified on the basis of their symmetry properties and of their orientation with respect to the symmetry elements of the point groups in which they occur.

General vs. special forms

A face is called general if only the identity operation transform the face onto itself. Each complete set of symmetrycally equivalent general faces is a general crystal form. The mulplicity (numer of faces of the form) of a general form is the order of the point group P. In the stereographic projection, the poles of general faces do not lie on any symmetry element of P.

A point is called general if its site symmetry is 1. A general point form is a complete set of symmetrically equivalent general points.

See also

• Chapter 10 in the International Tables for Crystallography, Volume A