Tilings of the sphere by congruent pentagons. II: Edge combination \(a^3b^2\). (English) Zbl 1484.52017
The authors continue their classification of edge-to-edge tilings of the two-dimensional sphere by congruent images of one spherical pentagon, see [E. Wang and M. Yan, Adv. Math. 394, Article ID 107866, 36 p. (2022; Zbl 1484.52016)]. In the present paper they characterize all tilings based on pentagons whose consecutive edges are of lengths \(a-a-a-b-b\) with different \(a,b\). They obtain five one parameter families and ten specific tilings.
For Part III, see [Y. Akama and the authors, ibid. 384, Article ID 107881, 41 p. (2022; Zbl 1484.52014)].
For Part III, see [Y. Akama and the authors, ibid. 384, Article ID 107881, 41 p. (2022; Zbl 1484.52014)].
Reviewer: Christian Richter (Jena)
MSC:
| 52C20 | Tilings in \(2\) dimensions (aspects of discrete geometry) |
| 05B45 | Combinatorial aspects of tessellation and tiling problems |
| 51M20 | Polyhedra and polytopes; regular figures, division of spaces |
PDFBibTeX
XMLCite
\textit{E. Wang} and \textit{M. Yan}, Adv. Math. 394, Article ID 107867, 68 p. (2022; Zbl 1484.52017)
References:
| [1] | Akama, Y.; Yan, M., On deformed dodecahedron tiling (2014), preprint |
| [2] | Akama, Y.; Wang, E. X.; Yan, M., Tilings of the sphere by congruent pentagons III: edge combination \(a^5 (2021)\), preprint |
| [3] | Gao, H. H.; Shi, N.; Yan, M., Spherical tiling by 12 congruent pentagons, J. Comb. Theory, Ser. A, 120, 4, 744-776 (2013) · Zbl 1272.52039 |
| [4] | H.P. Luk, M. Yan, Tilings of the sphere by congruent almost equilateral pentagons I: five distinct angles, preprint, 2021. |
| [5] | H.P. Luk, M. Yan, Tilings of the sphere by congruent almost equilateral pentagons II: three angles, preprint, 2021. |
| [6] | Wang, E. X.; Yan, M., Moduli of pentagonal subdivision tiling (2019), preprint |
| [7] | Wang, E. X.; Yan, M., Tilings of the sphere by congruent pentagons I: edge combinations \(a^2 b^2 c\) and \(a^3 b c (2021)\), preprint |
| [8] | Yan, M., Pentagonal subdivision, Electron. J. Comb., 26, Article P4.19 pp. (2019) · Zbl 1427.05047 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
