Harborth conjecture state that every planar graph can be drawn on a plane only using staight line segments of rational or integral edge length. ( There is a good mathoverflow page for this conjecture, Integral straight-line embeddings of planar graphs )

Due to Steinitz theorem, every 3-connected planar graph, so called polyhedral graph , can be realized as an edge graph of a convex polyhedron. Moreover, for every polyhedral graph, it turned out that we can find a realization in Euclidean 3-space only on integer coordinates.

My question is, in some sense, a variant of Harborth conjecture for Steinitz theorem, i.e.

Every polyhedral graph can be realized as a Euclidean convex polyhedron in which the edge lengths are all integers.

It still seems to be difficult to answer as like Harborth's original conjecture.

Have there been a study for this question?


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