Characterisation of geodesic self-dual regular surface triangulations

2019/10/22 by Baumeister, Markus
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1910.10112

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 ⟨ a,b,c| a²,b²,c²,(ab)³,(ac)²,(bc)^d⟩ that intersect ⟨ a,b⟩, ⟨ a,c⟩, and ⟨ b,c⟩ 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.

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