Tilings of the Sphere by Congruent Pentagons I

Abstract

We show that there are no edge-to-edge tilings of the sphere by congruent pentagons beyond the minimal dodecahedron tiling, such that there is a tile with all vertices having degree 3 and the edge length combinations are three of the five possibilities.

arXiv comment33 pages, 22 figures

References in corpus (4)

• Spherical Tiling by 12 Congruent Pentagons
• On Deformed Dodecahedron Tiling
• Tilings of the Sphere by Edge Congruent Pentagons
• Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons

Cited by in corpus (4)

• On Deformed Dodecahedron Tiling
• Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
• Tilings of the Sphere by Congruent Pentagons I: Edge Combinations $a^2{b}^{2}c$ and $a^{3}bc$
• Tilings of the Sphere by Congruent Quadrilaterals with Exactly Two Equal Edges