Coxeter Twisted Honeycomb {8,3}_8

This tilegraph consists of 42 octagonal tiles which form the following group $$G=\langle f_1, f_2, t_1, t_2, t_3 \mid f_1^2,f_2^2, t_2^{-1}f_2t_1^{-1}, t_1^3, t_3^{-1}t_2f_1, t_3^3, t_2^{-1}t_3^{-1}t_1f_1, t_2f_2t_3t_1^{-1}\rangle$$

It is dual to the twisted honeycomb {3,8}_8 described by Coxeter, where {p,q}_r means that q * p-gons meet at any vertex, while r is the size of the petrie polygon emanating in any direction. The number of automorphisms of the tilegraph without colouring is 1344.

The tiling and the discussion thereof by Coxeter in "Twisted Honeycombs" was brought to our attention by Chaim Goodman-Strauss.