Realizations of regular abstract polyhedra of types \(\{3,6\}\) and \(\{6,3\}\)
Regular abstract polyhedra are graded posets which generalize the face lattices of regular polytopes. They also cover non-spherical combinatorial manifolds which admit a flag transitive group action. The authors study a class of regular abstract polyhedra whose boundaries are \(2\)-dimensional tori. These arise as quotients of the regular triangular and hexagonal tilings of the Euclidean plane. The main result classifies geometric realizations of such polyhedra such that the automorphisms are isometries.
scientific article; zbMATH DE number 1507672