On Folding a Polygon to a Polyhedron

TL;DR

This paper clarifies that a longstanding open problem in geometric folding has been resolved by a theorem established over a decade earlier, linking origami and polyhedral folding.

Contribution

It demonstrates that a previously open problem in folding algorithms is actually solved by an existing theorem from Burago and Zalgaller, connecting origami and polyhedron folding.

Findings

The open problem in folding algorithms is resolved by Burago and Zalgaller's theorem.

The paper clarifies historical and theoretical connections in geometric folding.

It emphasizes the relevance of earlier mathematical results to modern folding problems.

Abstract

We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.