  We investigate necessary conditions for the existence of projections of
polytopes that preserve full k-skeleta. More precisely, given the combinatorics
of a polytope and the dimension e of the target space, what are obstructions to
the existence of a geometric realization of a polytope with the given
combinatorial type such that a linear projection to e-space strictly preserves
the k-skeleton. Building on the work of Sanyal (2009), we develop a general
framework to calculate obstructions to the existence of such realizations using
topological combinatorics. Our obstructions take the form of graph colorings
and linear integer programs. We focus on polytopes of product type and
calculate the obstructions for products of polygons, products of simplices, and
wedge products of polytopes. Our results show the limitations of constructions
for the deformed products of polygons of Sanyal & Ziegler (2009) and the wedge
product surfaces of R\"orig & Ziegler (2009) and complement their results.
