Tilings of the sphere by congruent quadrilaterals. III: Edge combination \(a^3b\) with general angles
type: Item
instance of: scholarly article
title: Tilings of the sphere by congruent quadrilaterals. III: Edge combination \(a^3b\) with general angles
author: Q6123014
author: Pinren Qian
author: Erxiao Wang
author: Y. Y. Xu
published in: Forum Mathematicum
publication date: 2024-10-01T00:00:00Z
review text: This is part III terminating the series of papers classifying all edge-to-edge tilings of the sphere by congruent quadrilaterals, started by \textit{Y. Liao} et al. [Chin. Ann. Math., Ser. B 45, No. 5, 733--766 (2024; Zbl 07938240)] and \textit{Y. Liao} and \textit{E. Wang} [Nagoya Math. J. 253, 128--163 (2024; Zbl 1545.52013)].\N\NAs final edge configuration the case \(a^3b\) is considered, i.e. tiles with three edges of equal length, with at least one angle an irrational multiple of \(\pi\). The main result is that on the one hand there are 5 sporadic cases among which 3 with 16 tiles and one of 12 and 24 tiles each; on the other hand, for each even number of tiles \(\geq 6\) a continuous 1-parameter family of 2-layer earth map a3b-tilings exist, together with a discrete number of flip modifications.\N\NThe paper ends with an overview of the complete classification of spherical edge-to-edge tilings by congruent quadrilaterals.
reviewed by: Frank Plastria
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 7920504
zbMATH Keywords: spherical tiling
zbMATH Keywords: quadrilateral
zbMATH Keywords: classification
zbMATH Keywords: Earth map tiling
zbMATH Keywords: irrational angle
MaRDI profile type: Publication
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DOI: 10.1515/FORUM-2023-0209
description: scientific article; zbMATH DE number 7920504