2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112839We show that the interior of the convex core of a quasifuchsian punctured-torus group admits an ideal decomposition (usually an infinite triangulation) which is canonical in two different senses: in a combinatorial sense via the pleating invariants, and in a geometric sense via an Epstein-Penner convex hull construction in Minkowski space. The result extends to certain non-quasifuchsian punctured-torus groups, and in fact to all of them if a strong version of the Pleating Lamination Conjecture is true.38 pages, 14 figuresGeometric TopologyMetric Geometry51F99 ; 51H20 ; 52B99 ; 57M50 ; 57M60text