Deltahedral Domes over Equiangular Polygons
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909685439791104 |
|---|---|
| author | MIT CompGeom Group Akitaya, Hugo A. Demaine, Erik D. Hesterberg, Adam Lubiw, Anna Lynch, Jayson O'Rourke, Joseph Stock, Frederick Tkadlec, Josef |
| author_facet | MIT CompGeom Group Akitaya, Hugo A. Demaine, Erik D. Hesterberg, Adam Lubiw, Anna Lynch, Jayson O'Rourke, Joseph Stock, Frederick Tkadlec, Josef |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deltahedral Domes over Equiangular Polygons MIT CompGeom Group Akitaya, Hugo A. Demaine, Erik D. Hesterberg, Adam Lubiw, Anna Lynch, Jayson O'Rourke, Joseph Stock, Frederick Tkadlec, Josef Metric Geometry 52C99 F.2.2; G.2.2 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. |
| title | Deltahedral Domes over Equiangular Polygons |
| topic | Metric Geometry 52C99 F.2.2; G.2.2 |
| url | https://arxiv.org/abs/2408.04687 |