Year: 2026
Type: article
Abstract: Can the sphere be tiled by an odd number of congruent polygons in an edge-to-edge arrangement? The answer is negative under a natural setting where polygons have at least 3 edges and at least 3 polygons meet at each vertex. The parity phenomenon has come to light after a voluminous classification of spherical tilings. We offer a short proof of it and draw a parallel to a result in polyhedra by Branko Grünbaum.
Source: Archiv der Mathematik
Author: Hoi Ping Luk
Institution: University of West Bohemia in Pilsen
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7141022813