English

Un-unzippable Convex Caps

Computational Geometry 2018-02-07 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.1802.01621,
  title  = {Un-unzippable Convex Caps},
  author = {Joseph O'Rourke},
  journal= {arXiv preprint arXiv:1802.01621},
  year   = {2018}
}

Comments

14 pages, 14 figures, 10 references

R2 v1 2026-06-23T00:11:56.682Z