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Which convex polyhedra can be made by gluing regular hexagons?

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.

preprint2020arXivOpen access
Elena ArsenevaStefan Langerman
Computational Geometry
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Elena ArsenevaStefan Langerman

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