- 
      Call
      
         Bravais_catalog
      Input family symbol 1,1,1,1,1, calculate the groups, choose file name 11111 and
      print all groups.
      The Bravais group <-I5> is written to file '11111'.
      Note, each Bravais group of degree 5 contains this group.
- 
      Call
      
         Bravais_inclusions 11111 -S > all
      Now the file 'all' contains a list of the names of all Bravais
      groups of degree 5, more precisely representatives of the Z-classes.
 (Note:
         grep Symbol all | wc
      would tell us that there are 189 Z-classes of Bravais groups of degree 5.)
- 
      Call
      
         Bravais_catalog
      Input family symbol 5-1, calculate the groups, choose file name 51 and print all groups.
      All Bravais groups in family 5-1 are now listed in file '51'.
 There are three Bravais groups in file '51' now. By irreducibility
      all three Bravais groups are maximal finite. Later we want to
      omit their proper Bravais subgroups from the file 'all'. To
      prepare this edit the file '51' and split it up into three
      files '51a', '51b' and '51c' containing one Bravais group each.
- 
      Call
      
         Bravais_catalog
      Input family symbol 5-2 calculate the groups, choose file name 52 and print all groups.
      All Bravais groups in family 5-1 are now listed in file '52'.
 There are four Bravais groups in file 52 now. By irreducibility
      all four Bravais groups are maximal finite. Later we want to
      omit their proper Bravais subgroups from the file 'all'. To
      prepare this edit the file '52' and split it up into four
      files '52a', '52b', '52c' and  '52d'
      containing one Bravais group each.
- 
      Call
      
         Bravais_inclusions 51a > notmax
         Bravais_inclusions 51b >> notmax
         Bravais_inclusions 51c >> notmax
         Bravais_inclusions 52a >> notmax
         Bravais_inclusions 52b >> notmax
         Bravais_inclusions 52c >> notmax
         Bravais_inclusions 52d >> notmax
      to write the names of the Bravais subgroups of the five maximal finite
      subgroups known so far on file 'notmax'.
- 
      Call
      
         grep Symbol notmax > compare
         sort -u compare > notmax
      Now the file 'notmax' contains the names of the seven maximal
      groups and of their proper Bravais subgroups, each one listed just once.
      By editing the file 'notmax', one writes the lines corresponding to
      maximal groups on a new file 'MAX. (These are the last seven lines.)
- 
      Call
      
         sort all > allsort
         diff allsort notmax | grep Symbol > all
      Now the file 'all' contains a complete list of Bravais groups,
      which are not contained in one of the groups of the file 'MAX'.
- 
      The last lines of the file 'all', more precisely the ones
      involving a symbol of the form 4-x;1 are the following:
      
         < Symbol: 4-1;1  homogeneously d.: 2 zclass: 1
         < Symbol: 4-2';1  homogeneously d.: 1 zclass: 1
         < Symbol: 4-2;1  homogeneously d.: 1 zclass: 1
         < Symbol: 4-2;1  homogeneously d.: 2 zclass: 1
         < Symbol: 4-3';1  homogeneously d.: 1 zclass: 1
         < Symbol: 4-3;1  homogeneously d.: 1 zclass: 1
         < Symbol: 4-3;1  homogeneously d.: 2 zclass: 1
      By using
         Bravais_inclusions -S
      one can rule out the two groups involving a ' as maximal finite
      groups. For the remaining five groups it is clear now that they
      are maximal finite. So by repeating the above computations with
      these five groups leads us to a new file 'MAX' containig 7+5
      groups and a new file 'all' containing all Bravais groups not
      contained in any of the groups in 'MAX' (up to Z-equivalence).
      It turns out that the process terminates after the next step
      with 'MAX' looking like
         5-1a       5-1c       5-2b       5-2d
         5-1b       5-2a       5-2c
         4-112   4-211   4-212   4-311   4-312
         32-11   32-13   32-21   32-22   32-23