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arXiv · 2110.10087

Tilings of the sphere by congruent quadrilaterals I: edge combination $a^2bc$

Yixi Liao·Pinren Qian·Erxiao Wang·Yingyun Xu
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Abstract

The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of quadrilateral subdivisions of the octahedron with $24$ tiles together with a flip modification for a special parameter, and a sequence of $3$-layer earth map tilings with $8n$ $(n\ge2)$ tiles together with two flip modifications for odd $n$. We also describe the moduli and calculate the geometric data.

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Yixi Liao, Pinren Qian, Erxiao Wang, Yingyun Xu. 2021-10-19. Tilings of the sphere by congruent quadrilaterals I: edge combination $a^2bc$. https://arxiv.org/abs/2110.10087

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