Year: 2019
Type: preprint
Abstract: We consider triangulations of closed surfaces in which every vertex is incident to exactly $d$ edges. These triangulations can be identified with subgroups of the triangle group $\langle a,b,c\mid a^2,b^2,c^2,(ab)^3,(ac)^2,(bc)^d\rangle$ that intersect $\langle a,b\rangle$, $\langle a,c\rangle$, and $\langle b,c\rangle$ trivially. The term geodesic duality refers to an external symmetry introduced by Wilson in 1979. Our main result is the characterisation of all subgroups corresponding to geodesic self--dual regular triangulations, together with a complete enumeration for $d < 10$.
Source: arXiv (Cornell University)
Author: Baumeister, Markus
Institution: RWTH Aachen University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2981568877