4 citations · 4 across the 12 of their papers we have counts for
12 papers
Dihedral Tilings of the Sphere by Kites and Regular Polygons
Robert Barish, Kam Hang Cheng, Hoi Ping Luk
In this article, we study the edge-to-edge dihedral tilings of the sphere by kites and regular -gons with . All such tilings have been identified and fully classified, u…
Tiling the Sphere with Regular Polygons
Hoi Ping Luk, Roman Nedela, Christopher Purcell
We give a complete classification of edge-to-edge tilings of the sphere by regular polygons under a unified framework. Without assuming convexity of the tiles or polyhedrality of t…
Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
Robert Barish, Hoi Ping Luk, Min Yan
Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be d…
Dihedral f-Tilings of the Sphere Induced by the Möbius Triangle
Catarina Avelino, Hoi Ping Luk, Altino Santos
We classify the special families of dihedral folding tilings of the sphere derived from the Möbius triangle . Our study emerges from the study of isometric foldings in the…
Dihedral Tilings of the Sphere by Regular Polygons and Quadrilaterals II: Regular Polygons with High Gonality and Rhombi
Ho Man Cheung, Hoi Ping Luk
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons with gonality at least 5 and rhombi.
Dihedral Tilings of the Sphere by Regular Polygons and Quadrilaterals I: Squares and Rhombi
Hoi Ping Luk
We classify the dihedral edge-to-edge tilings of the sphere by squares and rhombi.
Dihedral Tilings of the Sphere by Regular Polygons and Quadrilaterals I: Quadrilaterals with Equal Opposite Edges
Hoi Ping Luk
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons and quadrilaterals with equal opposite edges (edge configuration xyxy).
Tilings of the Sphere by Congruent Pentagons IV: Edge Combination
Hoi Ping Luk, Min Yan
We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edg…
Rational Angles and Tilings of the Sphere by Congruent Quadrilaterals
Ho Man Cheung, Hoi Ping Luk
We apply Diophantine analysis to classify edge-to-edge tilings of the sphere by congruent almost equilateral quadrilaterals (i.e., edge combination a3b). Parallel to a complete cla…
Tilings of the Sphere by Congruent Quadrilaterals or Triangles
Ho Man Cheung, Hoi Ping Luk, Min Yan
We completely classify edge-to-edge tilings of the sphere by congruent quadrilaterals. As part of the classification, we also present a modern version of the classification of edge…
Tilings of the Sphere by Congruent Quadrilaterals with Exactly Two Equal Edges
Ho Man Cheung, Hoi Ping Luk
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, -earth map t…
Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
Hoi Ping Luk, Min Yan
We develop a systematic method for computing the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method is a…