  Toric varieties play an important role both in symplectic and complex
geometry. In symplectic geometry, the construction of a symplectic toric
manifold from a smooth polytope is due to Delzant. In algebraic geometry, there
is a more general construction using fans rather than polytopes. However, in
case the fan is induced by a smooth polytope Audin showed both constructions to
give isomorphic projective varieties. For rational but not necessarily smooth
polytopes the Delzant construction was refined by Lerman and Tolman, leading to
symplectic toric orbifolds or more generally, symplectic toric DM stacks
(Lerman and Malkin). We show that the stacks resulting from the Lerman-Tolman
construction are isomorphic to the stacks obtained by Borisov et al. in case
the stacky fan is induced by a polytope. No originality is claimed (cf. also an
article by Sakai). Rather we hope that this text serves as an example driven
introduction to symplectic toric geometry for the algebraically minded reader.
