A d-zonotope is defined by a set VZ= { v1, ..., vD } of D positive vectors of a d-dimensional vector space such that any subset of d vectors in VZ is independent, and by a set of D integers { m1, ... , mD }. The zonotope Z is then the following set of points of the d-dimensional affine space: Z = { the Minkowski sum of the vectors i.e. the sum of ai vi, with 0 <= ai = mi }.
Each d-tile used to tile a d-zonotope Z is a d-zonotope defined by d vectors in VZ and with mi=1 for all i.
A d-tiling of a d-zonotope Z is a set of translated d-tiles such that
* the union of the translated d-tiles covers Z
* the interiors of the translated d-tiles are two-by-two disjoint.
The set of tilings of a decagon is flip-connected:
We can define a flip in all dimension: this is nothing but the two (d-1)-tilings of a d-zonotope with mi=1 for all i (i.e. the two (d-1)-tilings of an hypercube of dimension d)
