Which Convex Polyhedra Can Be Made by Gluing Regular Hexagons?
Graphs and Combinatorics(2019)
摘要
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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关键词
Polyhedral metrics,Alexandrov’s theorem,Gluings,Regular polygons
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