The monodromy group of a truncated simplex (Q887940)

The monodromy group of an abstract polytope is a certain permutation group on the flags of the polytope, and is a combinatorial invariant. Monodromy groups are generally difficult to compute. The authors show that the monodromy group of the truncated \(n\)-simplex \(T_n\) is isomorphic to the direct product of symmetric groups \(S_{n+1}\times S_n\), and is also isomorphic to the automorphism group of the unique minimal regular combinatorial cover of \(T_n\). A nice presentation for the group is also described.