I have an octagon (irregular) whose elements of symmetry I have found are;

s(oct) = {e, r(pi), q(pi/2), q(3*pi/4)}

I have to construct a Cayley table but have come to a halt part way through.

o.............. ...e.............r(pi).......q(pi/2)..................... .....e .............r(pi)....... q(pi/2) .......q(3*pi/4)q(3*pi/4)e

r(pi)............ r(pi)............ e........... q(7*pi/4) .......q ?

q(pi/2)....... q(pi/2)........ q?........... r ? ............r ?

q(3*pi/4.)..q(3*pi/4)..... q?........... r ? ............r ?

The quarters should have all the same type (r or q)

I'm trying to visualise it as a fixed point on a disc, but am still having trouble. Also can I use the "constant diagonal" to help & if so where?

Any helpful explanation as to whether I'm going about this the right way would be great