
TL;DR
This paper demonstrates that certain nearly flat convex caps, which are partial convex polyhedra with a boundary, do not admit an unzipping, highlighting limitations in unfolding convex shapes.
Contribution
It introduces the first examples of nearly flat convex caps that cannot be unzipped, advancing understanding of polyhedral unfolding limitations.
Findings
Nearly flat convex caps have no unzipping.
Unzipping remains an open problem for convex polyhedra.
The study identifies specific geometric configurations that prevent unzipping.
Abstract
An unzipping of a polyhedron P is a cut-path through its vertices that unfolds P to a non-overlapping shape in the plane. It is an open problem to decide if every convex P has an unzipping. Here we show that there are nearly flat convex caps that have no unzipping. A convex cap is a "top" portion of a convex polyhedron; it has a boundary, i.e., it is not closed by a base.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Geometric and Algebraic Topology · Advanced Materials and Mechanics
