  The simplicial wedge construction on simplicial complexes and simple
polytopes has been used by a variety of authors to study toric and related
spaces, including non-singular toric varieties, toric manifolds, intersections
of quadrics and more generally, polyhedral products. In this paper we extend
the analysis to include toric orbifolds. Our main results yield infinite
families of toric orbifolds, derived from a given one, whose integral
cohomology is free of torsion and is concentrated in even degrees, a property
which might be termed \emph{integrally equivariantly formal}. In all cases, it
is possible to give a description of the cohomology ring and to relate it to
the cohomology of the original orbifold.
