English

Regular maps of high density

Combinatorics 2015-01-15 v1

Abstract

A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and we conclude that all regular maps of this type belong to a family of maps naturally defined on the Fermat curves x^n+y^n+z^n=0, excepting the one corresponding to the tetrahedron.

Keywords

Cite

@article{arxiv.1501.03377,
  title  = {Regular maps of high density},
  author = {R. H. Eggermont and M. Hendriks},
  journal= {arXiv preprint arXiv:1501.03377},
  year   = {2015}
}

Comments

13 pages, 4 figures

R2 v1 2026-06-22T08:01:14.552Z