  We 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.
