Tilings of the sphere by congruent quadrilaterals I: edge combination $a^2bc$
| Autor: | Liao, Yixi, Qian, Pinren, Wang, Erxiao, Xu, Yingyun |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Final version: 44 pages, 42 figures, 2 tables. Thank two junior students Fangbin Chen and Nan Zhang for showing us how to draw Fig. 2 using GeoGebra. Thank one referee for the long and detailed suggestions so much, which essentially improved the writings |
| Databáze: | arXiv |
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