Type: Article

Mixing and monodromy of abstract polytopes

B. Monson; Daniel Pellicer; Gordon Williams;

Abstract:

The monodromy group of an -polytope encodes the combinatorial information needed to construct . By applying tools such as mixing, a natural group-theoretic operation, we develop various criteria for itself to be the automorphism group of a regular -polytope . We examine what this can say about regular covers of , study a peculiar example of a -polytope with infinitely many distinct, minimal regular covers, and then conclude with a brief application of our methods to chiral polytopes.