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pro vyhledávání: '"Luk, Hoi Ping"'
We classify the special families of dihedral folding tilings of the sphere derived from the M\"obius triangle $(2,3,4)$. Our study emerges from the study of isometric foldings in the Riemann sphere and meets at the juncture of the triangle group $\De
Externí odkaz:
http://arxiv.org/abs/2411.05973
Autor:
Cheung, Ho Man, Luk, Hoi Ping
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons with gonality at least 5 and rhombi.
Comment: 23 pages, 21 figures. arXiv admin note: text overlap with arXiv:2403.05941
Comment: 23 pages, 21 figures. arXiv admin note: text overlap with arXiv:2403.05941
Externí odkaz:
http://arxiv.org/abs/2403.07014
Autor:
Luk, Hoi Ping
We classify the dihedral edge-to-edge tilings of the sphere by squares and rhombi.
Comment: 21 pages, 21 figures
Comment: 21 pages, 21 figures
Externí odkaz:
http://arxiv.org/abs/2403.05941
Autor:
Luk, Hoi Ping
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons and quadrilaterals with equal opposite edges (edge configuration xyxy).
Comment: 17 pages, 13 figures
Comment: 17 pages, 13 figures
Externí odkaz:
http://arxiv.org/abs/2403.05938
Autor:
Luk, Hoi Ping, Yan, Min
We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral pentagons of
Externí odkaz:
http://arxiv.org/abs/2307.11453
Autor:
Cheung, Ho Man, Luk, Hoi Ping
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 classification by Cheung, Luk and Yan, the method implemented here is mor
Externí odkaz:
http://arxiv.org/abs/2204.02748
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-to-edge tilings of the sphere by congruent triangles. Together with o
Externí odkaz:
http://arxiv.org/abs/2204.02736
Autor:
Cheung, Ho Man, Luk, Hoi Ping
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral subdivisions of
Externí odkaz:
http://arxiv.org/abs/2108.06574
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Autor:
Luk, Hoi Ping, Yan, Min
We develop a systematic method for computing the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method is a useful and necessary step in many tiling problems about pentagonal til
Externí odkaz:
http://arxiv.org/abs/1308.4207