The regular polyhedra of type {p, 3} with 2pvertices

✍ Scribed by Peter McMullen

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 217 KB
• Volume: 43
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00151518

✦ Synopsis

THE REGULAR POLYHEDRA OF TYPE {p, 3} WITH 2p VERTICES 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.