Dihedral Tilings of the Sphere by Kites and Regular Polygons

Robert Barish; Kam Hang Cheng; Hoi Ping Luk

Dihedral Tilings of the Sphere by Kites and Regular Polygons

Combinatorics 2026-07-07 v1 Metric Geometry

Authors: Robert Barish , Kam Hang Cheng , Hoi Ping Luk

Abstract

In this article, we study the edge-to-edge dihedral tilings of the sphere by kites and regular $m$ -gons with $m\ge 4$ . All such tilings have been identified and fully classified, using various combinatorial and geometric tools. New phenomena are observed among the tilings.

Keywords

dihedral tilings sphere kites regular polygons classification edge-to-edge

Cite

@article{arxiv.2607.06798,
  title  = {Dihedral Tilings of the Sphere by Kites and Regular Polygons},
  author = {Robert Barish and Kam Hang Cheng and Hoi Ping Luk},
  journal= {arXiv preprint arXiv:2607.06798},
  year   = {2026}
}

Comments

49 pages, 49 figures