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arXiv · 2408.04687

Deltahedral Domes over Equiangular Polygons

MIT CompGeom Group·Hugo A. Akitaya·Erik D. Demaine·Adam Hesterberg·Anna Lubiw·Jayson Lynch·Joseph O'Rourke·Frederick Stock·Josef Tkadlec
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Abstract

A polyiamond is a polygon composed of unit equilateral triangles, and a generalized deltahedron is a convex polyhedron whose every face is a convex polyiamond. We study a variant where one face may be an exception. For a convex polygon P, if there is a convex polyhedron that has P as one face and all the other faces are convex polyiamonds, then we say that P can be domed. Our main result is a complete characterization of which equiangular n-gons can be domed: only if n is in {3, 4, 5, 6, 8, 10, 12}, and only with some conditions on the integer edge lengths.

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MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg, Anna Lubiw, Jayson Lynch, Joseph O'Rourke, Frederick Stock, Josef Tkadlec. 2024-08-08. Deltahedral Domes over Equiangular Polygons. https://arxiv.org/abs/2408.04687

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