@article{Liang2026, 
author = {Jinjin Liang and Yixi Liao and Erxiao Wang},
title = {Cyclotomic points on algebraic varieties and all rational        a    3    b-monotiles},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {8225-8241},
keywords = {root of unity, trigonometric Diophantine equation, cyclotomic point, spherical tiling, quadrilateral},
url = {https://www.sciopen.com/article/10.3934/math.2026338},
doi = {10.3934/math.2026338},
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.}
}