5 papers · 1 filter
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…
Tilings of Flat Tori by Congruent Hexagons
Xinlu Yu, Erxiao Wang, Min Yan
Convex hexagons that can tile the plane have been classified into three types. For the generic cases (not necessarily convex) of the three types and two other special cases, we cla…
Moduli Spaces of Pentagonal Subdivision Tilings
Jinjin Liang, Erxiao Wang, Min Yan
Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two dimensional moduli. We describe the moduli in deta…
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…
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…