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.
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Received February 14, 2000, and in revised form August 15, 2000. Online publication March 26, 2001.
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Datta, B., Nilakantan, N. Equivelar Polyhedra with Few Vertices. Discrete Comput Geom 26, 429–461 (2001). https://doi.org/10.1007/s00454-001-0008-0
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DOI: https://doi.org/10.1007/s00454-001-0008-0