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TILINGS OF THE SPHERE BY CONGRUENT QUADRILATERALS II: EDGE COMBINATION $a^3b$ WITH RATIONAL ANGLES
Ist Teil von
Nagoya mathematical journal, 2024-03, Vol.253, p.128-163
Ort / Verlag
Cambridge, UK: Cambridge University Press
Erscheinungsjahr
2024
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of
$a^3b$
-quadrilaterals with all angles being rational degrees. There are
$12$
sporadic and
$3$
infinite sequences of quadrilaterals admitting the two-layer earth map tilings together with their modifications, and
$3$
sporadic quadrilaterals admitting
$4$
exceptional tilings. Among them only three quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.