Skeletal configurations of ribbon trees

The straight skeleton construction creates a straight-line tree from a polygon. Motivated by moduli spaces from algebraic geometry, we consider the inverse problem of constructing a polygon whose straight skeleton is a given tree. We prove there exists only a finite set of planar embeddings of a tree appearing as straight skeletons of convex polygons. The heavy lifting of this result is performed by using an analogous version of Cauchy’s arm lemma. Computational issues are also considered, uncovering ties to a much older angle bisector problem.