Delaunay triangulations of lens spaces

Abstract

We compute the convex hull in ${\mathbb{C}}^2$ of an arbitrary finite subgroup of ${{\mathbb{C}}^{\ast }}^2$. The combinatorics are dictated by continued fractions in a natural way. This reproves a theorem of Smilansky, with a slightly stronger intermediary step.

16 pages, no figures. This second version mentions reference [S2], where the main result was already proved, and is extended to achieve the same level of generality as [S2]. Our key step (Claim 12) is slightly stronger than in [S2]