Abstract
G(p, d) is a cubic (3-valent) graph consisting of a p-gon and a (p/d)-gon (a starpolygon) with corresponding vertices joined (the notation admits anomalous cases, when d=1 or (d, p)>1), and with a high degree of symmetry. It is shown here that the seven possible graphs G(p, d) are just 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.
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McMullen, P. The regular polyhedra of type {p, 3} with 2p vertices. Geom Dedicata 43, 285–289 (1992). https://doi.org/10.1007/BF00151518
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DOI: https://doi.org/10.1007/BF00151518