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Computer software for construction of lattices of subgroups of N-dimensional space groups

Authors: Peter Engel⁺, Jiří Fuksa^#

⁺ Laboratory for Crystallography, Bern University, Freiestrasse 3, Bern, Switzerland

^# Institute of Physics, Acad. Sci. Czech Rep., Na Slovance 2, Praha, Czech Republic

Computer software „LAT_SUB“ is written in C language. It consists of three separate programs: calculation part (lr.exe), graphical interface (gr.exe) and interactive viewer (vwr.exe). The last two parts are written using Tcl-Tk (v.8.4.x) commands. Each part of the software can be compiled by gcc compiler (GNU Project) which is a standard part of any Linux OS.

The software constructs and, in a user-friendly manner, represents group-to-subgroup relationships among those subgroups of a given space group G~(P₁,T₁), which contain a specified subgroup H~(P₂,T₂) of a finite index. In other words, it displays the lattice of such subgroups. Illustrative Figure shows a part of the lattice of all subgroups of the space group No. 221 Pm-3m (with the normal subgroups highlighted).

The interactive viewer opens four windows, each displaying a lattice:

1. Lattice L₁ of relevant point groups P', P₂<P'<P₁

2. Lattice L₂ of relevant translation groups T', T₂<T'<T₁

3. Lattice L₃ of relevant crystallographic pairs (P',T'), where T' is invariant under the action of P', (P₂,T₂)<(P',T')<(P₁,T₁)

4. Lattice L₄ of all space groups H' ~ (P',T'), H~(P₂,T₂) < H'~(P',T') < G~(P₁,T₁)

On demand, lattices of normal subgroups are shown, or highlighted.

Note: The software packet is available for free. Please, let us know any bug that you may find (fuksa@fzu.cz). Your response will be helpful in supplying an updated version to the website. Thank you for your interest in our software,

Authors.