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^3b $-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.
Citation: Jinjin Liang, Yixi Liao, Erxiao Wang. Cyclotomic points on algebraic varieties and all rational $ a^3b $-monotiles[J]. AIMS Mathematics, 2026, 11(3): 8225-8241. doi: 10.3934/math.2026338
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^3b $-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.
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Jinjin Liang, Yixi Liao, Erxiao Wang. Cyclotomic points on algebraic varieties and all rational $ a^3b $-monotiles[J]. AIMS Mathematics, 2026, 11(3): 8225-8241. doi: 10.3934/math.2026338
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