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Research Article | Open Access

Cyclotomic points on algebraic varieties and all rational a 3 b-monotiles

Jinjin Liang, Yixi Liao, Erxiao Wang( )
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
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Abstract

By computing all cyclotomic points on specific algebraic varieties, we establish an independent and highly efficient method to determine the complete set of spherical a 3 b-monotiles with rational angles, thereby rigorously completing the classification of edge-to-edge monohedral quadrilateral tilings. Previous classification attempts relied heavily on fragmented older literature, within which several errors and logical gaps have been identified.

Keywords

root of unitytrigonometric Diophantine equationcyclotomic pointspherical tilingquadrilateral
CLC number: 05B45, 11R18, 11Y50, 14Q25, 52C20

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 8225-8241
DOI: 10.3934/math.2026338

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Cite this article:
Liang J, Liao Y, Wang E. Cyclotomic points on algebraic varieties and all rational a 3 b-monotiles. AIMS Mathematics, 2026, 11(3): 8225-8241. https://doi.org/10.3934/math.2026338

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Received: 23 December 2025
Revised: 28 February 2026
Accepted: 09 March 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)