Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals
Hoi Ping Luk,
Ho Man Cheung
Abstract:We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination $$a^3b$$
a
3
b
). Parallel to a complete classification by Cheung, Luk, and Yan, the method implemented here is more systematic and applicable to other related tiling problems. We also provide detailed geometric data for th… Show more
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