Some infinite families of finite incidence-polytopes (Q917914)

The author constructs infinite families of finite universal abstract regular polytopes, whose facets and vertex-figures are both regular maps whose types are specified by the lengths of their Petrie polygons. (The universality means that the facets and vertex-figures alone determine the polytopes.) These families are: \({}_ 4\{2n,4,3\}_ 6\), \({}_ 4\{4,2n,3\}_ 6\), \({}_ 4\{4,2n,4\}_ 4\), \({}_ 6\{3,2n,3\}_ 6\) and \({}_ 4\{3,3,2n\}_ 6\), for each \(n\geq 2\); the two suffixes refer to the Petrie polygons of the facet and vertex-figure, respectively.