# Limiting complex

A **limiting complex** is a lattice complex L1 which forms a true subset of a second lattice complex L2. Each point configuration of L1 also belongs to L2.

L2 is called a **comprehensive complex** of L1.

## Example

The Wyckoff *l* in the space-group type *P*4/*mmm*, with site-symmetry *m*2*m*., generates a lattice complex L1 that corresponds to point configurations consisting of squares in fixed orientation around the origin, with coordinates *x*00, -*x*00, 0*x*0 and 0-*x*0.

The Wyckoff position 4*j* in the space-group type *P*4/*m*, with site-symmetry *m*.., generates a lattice complex L2 that corresponds to point configurations consisting of squares in any orientation around the origin, with coordinates *xy*0, -*x-y*0, -*yx*0 and *y-x*0.

Among all the point configurations of L2 there is one, obtained by choosing *y* = 0, that corresponds to L1. The coordinates *x*00 in *P*4/*m* still correspond to Wyckoff position 4*j*, *i.e.* the specialization of the *y* coordinate does not change the Wyckoff position.

L1, occurring in *P*4/*mmm*, is *P*4/*m* as a *y* = 0: L1 is therefore a limiting complex of L2 and L2 is a comprehensive complex of L1.

### See also

- Chapter 14 of
*International Tables of Crystallography, Section A*