1. ## Dihedral Groups

In the dihedral group D4, what are the permutations? Is there a permutation that can’t be a rigid motion? explain.

2. Originally Posted by jjbrian
In the dihedral group D4, what are the permutations?
There are eight of them. Start counting. The usual representation in terms of generators and relations is $\sigma^2=e,\tau^{4}=e$

Is there a permutation that can’t be a rigid motion? explain.
This is more of an interpretation of the group (how it acts on a square) then what it really is.