26 research outputs found
Tilings of the sphere by congruent quadrilaterals II: edge combination with rational angles
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
-quadrilaterals with all angles being rational degrees. There are
sporadic and infinite sequences of quadrilaterals admitting the -layer
earth map tilings together with their modifications, and sporadic
quadrilaterals admitting exceptional tilings. Among them only
quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings
are obtained as a byproduct.Comment: 36 pages, 36 figures, 10 table