Degree-regular triangulations of the double-torus

Datta, Basudeb ; Upadhyay, Ashish Kumar (2006) Degree-regular triangulations of the double-torus Forum Mathematicum, 18 (6). pp. 1011-1025. ISSN 0933-7741

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Official URL: http://www.reference-global.com/doi/abs/10.1515/FO...

Related URL: http://dx.doi.org/10.1515/FORUM.2006.051

Abstract

A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinatorial 2-manifold of Euler characteristic -2 must contain 12 vertices. In 1982, McMullen et al. constructed a 12-vertex geometrically realized triangulation of the double-torus in R3. As an abstract simplicial complex, this triangulation is a weakly regular combinatorial 2-manifold. In 1999, Lutz showed that there are exactly three weakly regular orientable combinatorial 2-manifolds of Euler characteristic -2. In this article, we classify all the orientable degree-regular combinatorial 2-manifolds of Euler characteristic -2. There are exactly six such combinatorial 2-manifolds. This classifies all the orientable equivelar polyhedral maps of Euler characteristic -2.

Item Type:Article
Source:Copyright of this article belongs to Walter de Gruyter GmbH & Co. KG..
ID Code:75108
Deposited On:21 Dec 2011 14:11
Last Modified:21 Dec 2011 14:11

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