NAME
CM::Group::Dihedral - An implementation of the finite dihedral group D_2n
VERSION
version 0.94
DESCRIPTION
This group is formed of the reflectional and rotational symmetries of a regular polygon with n edges. It is also the symmetry group of a regular polygon.
SYNOPSIS
use CM::Group::Dihedral;
my $g = CM::Group::Dihedral->new({n=>10});
$g->compute;
print "$g";
1 10 9 8 7 6 5 4 3 2 19 18 17 16 15 14 13 12 11 20
2 1 10 9 8 7 6 5 4 3 18 17 16 15 14 13 12 11 20 19
3 2 1 10 9 8 7 6 5 4 17 16 15 14 13 12 11 20 19 18
4 3 2 1 10 9 8 7 6 5 16 15 14 13 12 11 20 19 18 17
5 4 3 2 1 10 9 8 7 6 15 14 13 12 11 20 19 18 17 16
6 5 4 3 2 1 10 9 8 7 14 13 12 11 20 19 18 17 16 15
7 6 5 4 3 2 1 10 9 8 13 12 11 20 19 18 17 16 15 14
8 7 6 5 4 3 2 1 10 9 12 11 20 19 18 17 16 15 14 13
9 8 7 6 5 4 3 2 1 10 11 20 19 18 17 16 15 14 13 12
10 9 8 7 6 5 4 3 2 1 20 19 18 17 16 15 14 13 12 11
11 20 19 18 17 16 15 14 13 12 9 8 7 6 5 4 3 2 1 10
12 11 20 19 18 17 16 15 14 13 8 7 6 5 4 3 2 1 10 9
13 12 11 20 19 18 17 16 15 14 7 6 5 4 3 2 1 10 9 8
14 13 12 11 20 19 18 17 16 15 6 5 4 3 2 1 10 9 8 7
15 14 13 12 11 20 19 18 17 16 5 4 3 2 1 10 9 8 7 6
16 15 14 13 12 11 20 19 18 17 4 3 2 1 10 9 8 7 6 5
17 16 15 14 13 12 11 20 19 18 3 2 1 10 9 8 7 6 5 4
18 17 16 15 14 13 12 11 20 19 2 1 10 9 8 7 6 5 4 3
19 18 17 16 15 14 13 12 11 20 1 10 9 8 7 6 5 4 3 2
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
$g->rearrange; # we rearrange so that identity sits on the first diagonal
print "$g";
1 10 9 8 7 6 5 4 3 2 19 18 17 16 15 14 13 12 11 20
2 1 10 9 8 7 6 5 4 3 18 17 16 15 14 13 12 11 20 19
3 2 1 10 9 8 7 6 5 4 17 16 15 14 13 12 11 20 19 18
4 3 2 1 10 9 8 7 6 5 16 15 14 13 12 11 20 19 18 17
5 4 3 2 1 10 9 8 7 6 15 14 13 12 11 20 19 18 17 16
6 5 4 3 2 1 10 9 8 7 14 13 12 11 20 19 18 17 16 15
7 6 5 4 3 2 1 10 9 8 13 12 11 20 19 18 17 16 15 14
8 7 6 5 4 3 2 1 10 9 12 11 20 19 18 17 16 15 14 13
9 8 7 6 5 4 3 2 1 10 11 20 19 18 17 16 15 14 13 12
10 9 8 7 6 5 4 3 2 1 20 19 18 17 16 15 14 13 12 11
19 18 17 16 15 14 13 12 11 20 1 10 9 8 7 6 5 4 3 2
18 17 16 15 14 13 12 11 20 19 2 1 10 9 8 7 6 5 4 3
17 16 15 14 13 12 11 20 19 18 3 2 1 10 9 8 7 6 5 4
16 15 14 13 12 11 20 19 18 17 4 3 2 1 10 9 8 7 6 5
15 14 13 12 11 20 19 18 17 16 5 4 3 2 1 10 9 8 7 6
14 13 12 11 20 19 18 17 16 15 6 5 4 3 2 1 10 9 8 7
13 12 11 20 19 18 17 16 15 14 7 6 5 4 3 2 1 10 9 8
12 11 20 19 18 17 16 15 14 13 8 7 6 5 4 3 2 1 10 9
11 20 19 18 17 16 15 14 13 12 9 8 7 6 5 4 3 2 1 10
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
These are labels of the elements and not the elements themselves(which internally are represented as permutations).
You can also see a coloured Cayley table(the labels of the permutations are associated to colours):
This is the Cayley graph of D_5:
AUTHOR
Stefan Petrea, <stefan.petrea at gmail.com>