Geometriae Dedicata

, Volume 43, Issue 3, pp 285–289 | Cite as

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

  • Peter McMullen


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.


Symmetry Group Regular Polyhedron Anomalous Case 
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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Peter McMullen
    • 1
  1. 1.Department of MathematicsUniversity College LondonLondonUK

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