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Discrete & Computational Geometry

, Volume 26, Issue 3, pp 429–461 | Cite as

Equivelar Polyhedra with Few Vertices

  • B. Datta
  • N. Nilakantan
Article

Abstract

We know that the polyhedra corresponding to the Platonic solids are equivelar. In this article we have classified completely all the simplicial equivelar polyhedra on ≤ 11 vertices. There are exactly 27 such polyhedra. For each n\geq -4 , we have classified all the (p,q) such that there exists an equivelar polyhedron of type {p,q} and of Euler characteristic n . We have also constructed five types of equivelar polyhedra of Euler characteristic -2m , for each m\geq 2.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • B. Datta
    • 1
  • N. Nilakantan
    • 1
  1. 1.Department of Mathematics, Indian Institute of Science, Bangalore 560\,012, India {dattab,nandini}@math.iisc.ernet.inIndia

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