CARAT Introduction / Examples / Find all Bravaisgroups of degree 6 consisting of permutation matrices and their negatives only.
Author: Oliver Heidbüchel
Description: CARAT Introduction: Example 8 - Find all Bravaisgroups of degree 6 consisting of permutation matrices and their negatives only.
Keywords: CARAT, crystallography, bravaisgroup, bravaisgroups, bravais groups, bravais group, mathematics, algorithms, tables, algorithm, table, examples, example, Aut_grp, Bravais_inclusions, permutation matrices, permutation matrix, matrix, permutation, permutations

Previous Example | Introduction | Next Example

### Example 8

Find all Bravaisgroups of degree 6 consisting of permutation matrices and their negatives only.

### Used Programs

Aut_grp, Bravais_inclusions

### Solution

1. Prepare the following file 'f' containing a basis of the space of invariant forms of the Bravais group B of all permutation matrices and their negatives.

             #2
             6 d0
             1
             6x0
             1
             1 1
             1 1 1
             1 1 1 1
             1 1 1 1 1
             1 1 1 1 1 1

2. Call

                Aut_grp f > gf

   to get all the relevant data of the Bravais group B on file 'gf'.
3. Call

                Bravais_inclusions gf > gfi

   to get all the Bravais subgroups of B on the file 'gfi', more precisely a list of the representatives of their conjugacy classes under the normalizer of B in GLn(Z), which is B itself.
   (Note, the above command only lists names. If one wants the actual groups, one has to call "Bravais_inclusions" with the option -G . This takes much longer.)
4. Call

                grep Symbol gfi | wc

   to count 27 subgroups.

Previous Example | Introduction | Next Example

last change: 11.09.2000