
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 <I_{5}> 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 Zclasses.
(Note:
grep Symbol all  wc
would tell us that there are 189 Zclasses of Bravais groups of degree 5.)

Call
Bravais_catalog
Input family symbol 51, calculate the groups, choose file name 51 and print all groups.
All Bravais groups in family 51 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 52 calculate the groups, choose file name 52 and print all groups.
All Bravais groups in family 51 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 4x;1 are the following:
< Symbol: 41;1 homogeneously d.: 2 zclass: 1
< Symbol: 42';1 homogeneously d.: 1 zclass: 1
< Symbol: 42;1 homogeneously d.: 1 zclass: 1
< Symbol: 42;1 homogeneously d.: 2 zclass: 1
< Symbol: 43';1 homogeneously d.: 1 zclass: 1
< Symbol: 43;1 homogeneously d.: 1 zclass: 1
< Symbol: 43;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 Zequivalence).
It turns out that the process terminates after the next step
with 'MAX' looking like
51a 51c 52b 52d
51b 52a 52c
4112 4211 4212 4311 4312
3211 3213 3221 3222 3223