A criterion for the affine equivalence of cell complexes in $R^d$ and convex polyhedra in $R^{d+1}$

F. Aurenhammer

Abstract:

A criterion is gives that decides, for a convex tiling $C$ of $R^d$, whether $C$ is the projection of the faces in the boundary of some convex polyhedron $P$ in $R^{d+1}$. Its applicability is restricted neither by the properties nor by the dimension of $C$. It turns out to be 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 construct $P$ provided it exists.



Reference: F. Aurenhammer. A criterion for the affine equivalence of cell complexes in $R^d$ and convex polyhedra in $R^{d+1}$. Discrete & Computational Geometry, 2(1):49-64, 1987. [IIG-Report-Series 205, TU Graz, Austria, 1985].