1.46: Form
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. The inherent symmetry of a form is a point group C which either coincides with the generating point group P or is a supergroup of it.
Forms in point groups correspond to crystallographic orbits in space groups.