  In the classical theory of toric manifolds polytopes appear in two guises --
as Newton polytopes of line bundles on the complex, and as moment polytopes on
the symplectic side, the link between the two being established by the
prequantizability condition on the cohomology class of the symplectic form.
  Here we give a combinatorial description of the orbifold Picard group for
complete toric orbifolds, with the aim of detailing the relation between
complex and symplectic aspects in the orbifold setting. In particular this
permits to illustrate the breakdown of identification of (orbifold) line
bundles by their Chern class (or moment polytope up to translations in
$\mathfrak{t}^\ast$), and non-constancy of $h^0$ on representatives of the same
Chern class. As an application, we discuss symplectic reduction with respect to
restrictions of the action to sub-tori, and the associated Bohr--Sommerfeld
conditions in mixed polarizations.
