TILINGS BY RELATED ZONOTOPES

We study periodic tilings of d-dimensional space by clusters of relate d zonotopes. For such tilings, the fundamental region relative to a fu lly-dimensional translation group is the finite union of zonotopes con structed as Minkowski sums of subsets of a given set of generating vec tors. For any rationally-realizable zonotope Z, the rational realizati on itself determines a unique periodic tiling in which one of the cell s is the zonotope Z. In an effort to find analogous tilings using nonr ational zonotopes, we conjecture a characterization in terms of a new family oriented matroid structures, for which we provide axioms.