A Definition of Type Domain of a Parallelotope

Each convex polytope $P=P(\alpha)$ can be described by a set of linear inequalities determined by vectors $p$ and right hand sides $\alpha(p)$. For a fixed set of vectors $p$, a type domain ${\mathcal D}(P_0)$ of a polytope $P_0$ and, in particular, of a parallelotope $P_0$ is defined as a set of parameters $\alpha(p)$ such that polytopes $P(\alpha)$ have the same combinatorial type as $P_0$ for all $\alpha\in{\mathcal D}(P_0)$.
In the second part of the paper, a facet description of zonotopes and zonotopal parallelotopes are given.
The article is published in the author's wording.