Zonotopes are convex polytopes that can be defined in several equivalent ways: parallel projections of cubes, Minkowsi sums of line segments, only centrally symmetric faces, ... I wonder whether there exists a calssification of all vertex-transitive zonotopes. I know only of the following exa...

A zonotope is a polytope whose 2-faces are centrally symmetric. Question: If a polytope $P$ is centrally symmetric and combinatorially equivalent to a zonotope, is it itself a zonotope?

General polytopes are not determined by their edge-graph (up to combinatorial equivalence). But I came accross the statement that zonotopes are determined in this way. Question: Is this true? And where is this proven? I suppose that this is somehow proven in the language of oriented matroids an...

For any set $P,Q$ in the Euclid space, define Minkowski sum '+' as follows: $P+Q=\{p+q|p\in P, q\in Q\}$. And define 'zonotope': a zonotope is the Minkowski sum of some (finite) segments (for example, parallelograms). In the 4-dimension Euclid space, $A=\{\operatorname{conv}(P\cup Q)\mid P, Q \t...

I have a question regarding the papers on approximating zonoids with zonotopes. I'll first write down the approximation problem and then state what my question is. Problem of Approximating Zonoids. Suppose that $Z\subseteq \mathbb{R}^d$ is a given zonoid, having the origin as an interior point an...