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May 14, 2021 at 20:31 comment added Hugh Thomas Since the OP mentions two polytopes, it might be helpful to clarify that the truncated octahedron is the Cayley graph of the symmetric group, while the truncated cuboctahedron is the Cayley graph of the Coxeter quotient of the group described by generators and relations at the end of the post.
May 14, 2021 at 13:01 history answered IJL CC BY-SA 4.0