ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

Degree-regular triangulations of the double-torus

Datta, B and Upadhyay, AK (2006) Degree-regular triangulations of the double-torus. In: Forum Mathematicum, 18 (6). pp. 1011-1025.

[img] PDF
Degree-regular_triangulations.pdf - Published Version
Restricted to Registered users only

Download (180kB) | Request a copy
Official URL: http://arxiv.org/abs/math/0508106


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 R-3. 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: Journal Article
Publication: Forum Mathematicum
Publisher: Walter de Gruyter GmbH & Co. KG
Additional Information: Copyright of this article belongs to Walter de Gruyter GmbH & Co. KG.
Keywords: Triangulations of 2-manifolds;regular simplicial maps; combinatorially regular triangulations;degree-regular triangulations.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 07 Aug 2007
Last Modified: 24 Jan 2012 05:36
URI: http://eprints.iisc.ac.in/id/eprint/11416

Actions (login required)

View Item View Item