Some Semi - Equivelar Maps
Geometric Topology
2011-01-18 v2 Combinatorics
Abstract
Semi-Equivelar maps are generalizations of Archimedean Solids (as are equivelar maps of the Platonic solids) to the surfaces other than Sphere. We classify some semi equivelar maps on surface of Euler characteristic -1 and show that none of these are vertex transitive. We establish existence of 12-covered triangulations for this surface. We further construct double cover of these maps to show existence of semi-equivelar maps on the surface of double torus. We also construct several semi-equivelar maps on the surfaces of Euler characteristics -8 and -10 and on non-orientable surface of Euler characteristics -2.
Cite
@article{arxiv.1101.0671,
title = {Some Semi - Equivelar Maps},
author = {Ashish K. Upadhyay and Anand K. Tiwari and Dipendu Maity},
journal= {arXiv preprint arXiv:1101.0671},
year = {2011}
}
Comments
20 pages, 2 figures, Revised, Examples condensed in tabular form