JOURNAL ARTICLE

TILINGS OF THE SPHERE BY CONGRUENT QUADRILATERALS II: EDGE COMBINATION $a^3b$ WITH RATIONAL ANGLES.

  • Published In: Nagoya Mathematical Journal, 2024, v. 253. P. 128 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Liao, Yixi; Wang, Erxiao 3 of 3

Abstract

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Nagoya Mathematical Journal. 2024/03, Vol. 253, p128
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2024
  • ISSN:0027-7630
  • DOI:10.1017/nmj.2023.20
  • Accession Number:175757043
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