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What is the graph diameter of the 1-skeleton of the omnitruncate of the $E_8$ family of uniform 8-polytopes?

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Since the 1-skeleton of this polytope is just the Cayley graph of the Coxeter group $E_8$ w.r.t. the usual set of generators, this diameter should equal the length of the longest element in the group, which is 120 according to this answer.

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