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math.CO2022
Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals
Ho Man Cheung, Hoi Ping Luk
We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete cla…
math.CO2022
Tilings of the Sphere by Congruent Quadrilaterals or Triangles
Ho Man Cheung, Hoi Ping Luk, Min Yan
We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge…