  In this paper, we introduce polytopal $k$-wedge construction and blowdown of
a simple polytope and inspect the effect on the retraction sequence of a simple
polytope due to $k$-wedge construction and blowdown. In relation to this
construction, we introduce the $k$-wedge and blowdown of a quasitoric orbifold.
We compare the torsions in the integral cohomologies of $k$-wedges and
blowdowns of a quasitoric orbifold with the original one. These two
constructions provide infinitely many integrally equivariantly formal
quasitoric orbifolds from a given one.
