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We study certain structural properties of fine zonotopal tilings, orcubillages, on cyclic zonotopes $Z(n,d)$ of an arbitrary dimension $d$ andtheir relations to $(d-1)$-separated collections of subsets of a set$\{1,2,\ldots,n\}$. (Collections of this sort are well known as stronglyseparated ones when $d=2$, and as chord separated ones when $d=3$.)

Cubillages on cyclic zonotopes, membranes, and higher separatation