  The goal of this paper is to classify symplectic toric stratified spaces with
isolated singularities. This extends a result of Burns, Guillemin, and Lerman
which carries out this classification in the compact connected case. In making
this classification, it is necessary to classify symplectic toric cones. Via a
well-known equivalence between symplectic toric cones and contact toric
manifolds, this allows for the classification of contact toric manifolds as
well, extending Lerman's classification of compact connected contact toric
manifolds.
