The Rest of the Tilings of the Sphere by Regular Polygons
Colin Adams, Cameron Edgar, Peter Hollander, Liza Jacoby
TL;DR
This paper classifies all possible non-edge-to-edge tilings of a sphere using regular polygons with three or more sides, expanding understanding of spherical tiling arrangements.
Contribution
It provides a complete enumeration of non-edge-to-edge spherical tilings by regular polygons, a problem not fully addressed before.
Findings
All such tilings are explicitly characterized.
The classification includes previously unknown tiling configurations.
Results contribute to the mathematical understanding of spherical geometry.
Abstract
We determine all non-edge-to-edge tilings of the sphere by regular spherical polygons of three or more sides.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Mathematics and Applications · Advanced Materials and Mechanics