Has there been something written about the following question?
Question: Given a 0/1-polytope, what is the shortest edge lengths with which this polytope can be realized as a 0/1-polytope.
The realization shall respect the angles of the polytope, so not only the combinatorial type.
Example. The regular $n$-crosspolytope can be realized (asymptotically) with edge length $$\ell\ge \sqrt{n/2},$$ but not shorter.
