is every edge of a zonotope a generator? Given a Zonotope $Z \subset \mathbb{R}^d$, with generators $G \in \mathbb{R}^{n\times d}$.
Every facet is a $d-1$ polytope. And I'm wondering is it true that every edge of the facets is one generator with some positional offset?
Since every vertex is in the form of $\sum_{i \in G} = \lambda_i i, \lambda_i \in \{0, 1\}$, and the edge is difference between two vertices, so every edge has to be some sum of a subset of generators. But does the difference has to be exactly one generator?

The answer is yes. And here is the proof:
If the edge is composed of more than one generator, one can always add an extra vertex correspondingly.
