The regular polyhedra of type \(\{p,3\}\) with \(2p\) vertices (Q1196143)

The author considers generalizations \(G(p,d)\) of the Petersen graph \(G(5,2)\) where the (simple) graph consists of a \(p\)-gon and a \((p/d)\)-gon (a star polygon) with corresponding vertices joined, and rich in symmetries. He proves that the seven possible graphs are the edge graphs of the regular polyhedra of type \(\{p,3\}\) with \(2p\) vertices, and therefore \(3p\) edges, 6 faces, and symmetry group of order \(12p\).