Deltahedral Domes over Equiangular Polygons
Metric Geometry
2025-07-15 v2
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.
Keywords
Cite
@article{arxiv.2408.04687,
title = {Deltahedral Domes over Equiangular Polygons},
author = {MIT CompGeom Group and Hugo A. Akitaya and Erik D. Demaine and Adam Hesterberg and Anna Lubiw and Jayson Lynch and Joseph O'Rourke and Frederick Stock and Josef Tkadlec},
journal= {arXiv preprint arXiv:2408.04687},
year = {2025}
}
Comments
25 pages, 19 figures, 8 references. v2 includes referee corrections