2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217900We compute the convex hull in $\mathbb{C}^2$ of an arbitrary finite subgroup of ${\mathbb{C}^*}^2$. 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]Geometric Topology52B11; 57M50text