Tilings of the sphere by congruent quadrilaterals III: edge combination a³b with general angles

2022/06/30 by Yixi Liao, Liao, Yixi, Pinren Qian +5 · 2 citations
Materials Science · Engineering · Mathematics · #Quasicrystal Structures and Properties #Advanced Materials and Mechanics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2206.15342

Abstract

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of a³b-quadrilaterals with some irrational angle: there are a sequence of 1-parameter families of quadrilaterals admitting 2-layer earth map tilings together with their basic flip modifications under extra condition, and 5 sporadic quadrilaterals each admitting a special tiling. A summary of the full classification is presented in the end.

Cited by

• Cyclotomic points on varieties and all rational a³b-monotiles
• Non-side-to-side tilings of the sphere by congruent triangles with any irrational angle

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