Minimal Covers of the Archimedean Tilings, Part 1

Abstract

We discuss representations of non-finite polyhedra as quotients of regular polytopes. We provide some structural results about the minimal regular covers of non-finite polyhedra and about the stabilizer subgroups of their flags under the flag action of the automorphism group of the covering polytope. As motivating examples we discuss the minimal regular covers of the Archimedean tilings, and we construct explicit minimal regular covers for three of them.