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.

Original languageEnglish
Pages (from-to) 339-345
Number of pages7
JournalGraphs and Combinatorics
Volume36
Issue number2
DOIs
StatePublished - 1 Mar 2020

    Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

    Research areas

  • Alexandrov’s theorem, Gluings, Polyhedral metrics, Regular polygons, Alexandrov's theorem

ID: 48856212