Faithful transitive permutation representations of C-groups

The study of regular objects, such as polytopes, and their symmetries is a subject that attracts researchers from different areas of mathematics, such as geometers and algebraists, but also researchers from other areas of knowledge such as chemistry, thanks to the high symmetry of the molecules. An abstract polytope is a structure that combinatorically describes a classical polytope. Abstract regular polytopes can be described as a poset, as an incidence geometry or as C-group with linear diagram. A hypertope was introduced as a polytope-like structure where its group of symmetries is a C-group however it does not need to have a linear diagram. The groups of these structures can be represented as faithful transitive permutation representation graphs.