Which convex polyhedra can be made by gluing regular hexagons?

2020/02/06 by Elena Arseneva, Stefan Langerman, Arseneva, Elena +1
Computer Science · Engineering · #Advanced Materials and Mechanics #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Computer and information sciences

paper · pdf · doi:10.48550/arxiv.2002.02052

openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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