A criterion for the affine equivalence of cell complexes inR d and convex polyhedra inR d+1

A criterion is given that decides, for a convex tilingC ofR^d, whetherC is the projection of the faces in the boundary of some convex polyhedronP inR^d+1. Its applicability is restricted neither by the properties nor by the dimension ofC. It turns out to be conceptually simpler than other criteria and allows the easy examination of various classes of cell complexes. In addition, the criterion is constructive, that is, it can be used to constructP provided it exists.Research was supported by the Austrian Fonds zur Foerderung der wissenschaftlichen Forschung.