English

Which convex polyhedra can be made by gluing regular hexagons?

Computational Geometry 2020-02-07 v1

Abstract

Which convex 3D polyhedra can be obtained by gluing several regular hexagons edge-to-edge? It turns out that there are only 15 possible types of shapes, 5 of which are doubly-covered 2D polygons. We give examples for most of them, including all simplicial and all flat shapes, and give a characterization for the latter ones. It is open whether the remaining can be realized.

Keywords

Cite

@article{arxiv.2002.02052,
  title  = {Which convex polyhedra can be made by gluing regular hexagons?},
  author = {Elena Arseneva and Stefan Langerman},
  journal= {arXiv preprint arXiv:2002.02052},
  year   = {2020}
}

Comments

7 pages, 5 figures

R2 v1 2026-06-23T13:32:33.747Z