# Equivelar Polyhedra with Few Vertices

Datta, B and Nilakantan, N (2001) Equivelar Polyhedra with Few Vertices. In: Discrete and Computational Geometry, 26 (3). pp. 429-461.

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## 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 \leq 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 $m \geq 2$.

Item Type: Journal Article Copyright of this article belongs to Springer. Division of Physical & Mathematical Sciences > Mathematics 18 Jul 2008 19 Sep 2010 04:47 http://eprints.iisc.ernet.in/id/eprint/15117