# Symmetry groups and Cayley table

Given an irregular octagon $O$ with vertices $(6,2)$, $(2,6)$, $(-1,5)$, $(-5,1)$, $(-6,-2)$, $(-2,-6)$, $(1, -5)$ and $(5,-1)$, what are the elements of the symmetry group $S(O)$ of $O$ in standard notation, and what would be the geometric effect of each symmetry on points in the plane? Also, what would the Cayley table for $S(O)$ be?

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A plot might help. –  joriki Oct 10 '12 at 17:28
@joriki Only rep 1 so can't add images. Could you edit and add plot? Thanks. –  oisyutat Oct 10 '12 at 17:32
@joriki That link might not show any plot for some users. –  rschwieb Oct 10 '12 at 17:35
@rschwieb: Why might that be? –  joriki Oct 10 '12 at 17:52
@oisyutat: My comment already contains a link to a plot; feel free to edit it into the question if you find it helpful. –  joriki Oct 10 '12 at 17:53