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