# Realizing 0/1-polytopes with shortest possible edge lengths

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.