The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings (Q1572873)

\textit{B. Sturmfels} [J. Algebr. Comb. 3, No. 2, 207-236 (1994; Zbl 0798.05074)] has established an order-preserving bijection between the posets of coherent mixed subdivisions of a Minkowski sum of point configurations in \(\mathbb R^d\) and of coherent polyhedral subdivisions of the associated Cayley embedding -- the polyhedral version of the Cayley trick of elimination theory. The authors generalize this relationship in the case of non-coherent subdivisions. As an application, a new proof is given of the Bohne-Dress theorem on zonotopal tilings.