24 citations · 58 across the 15 of their papers we have counts for
16 papers
Tilings of Closed Surfaces by Congruent Most Curvilinear Polygons
Haofang Sun, Min Yan
We study tilings of closed surfaces by congruent most curvilinear polygons. By relating such tilings to branched coverings determined by planar diagrams and vertex types, we establ…
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…
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…
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…
Pentagonal Subdivision
Min Yan
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions relate…
Tilings of the Sphere by Congruent Pentagons II: Edge Combination
Erxiao Wang, Min Yan
There are fifteen edge-to-edge tilings of the sphere by congruent pentagons with the edge combination : five one-parameter families of pentagonal subdivision tilings, and t…
Tilings of the Sphere by Congruent Pentagons III: Edge Combination
Yohji Akama, Erxiao Wang, Min Yan
There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings wi…
Tilings of the Sphere by Congruent Pentagons I: Edge Combinations and
Erxiao Wang, Min Yan
We develop the basic tools for classifying edge-to-edge tilings of the sphere by congruent pentagons. Then we prove that, for the edge combination , such tilings are three…
On Deformed Dodecahedron Tiling
Yohji Akama, Min Yan
There is only one type of tilings of the sphere by congruent pentagons. These tilings are isohedral.
Tilings of the Sphere by Congruent Pentagons I
Ka Yue Cheuk, Ho Man Cheung, Min Yan
We show that there are no edge-to-edge tilings of the sphere by congruent pentagons beyond the minimal dodecahedron tiling, such that there is a tile with all vertices having degre…
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…
Tilings of the Sphere by Edge Congruent Pentagons
Ka Yue Cheuk, Ho Man Cheung, Min Yan
We study edge-to-edge tilings of the sphere by edge congruent pentagons, under the assumption that there are tiles with all vertices having degree 3. We develop the technique of ne…
Combinatorial Tilings of the Sphere by Pentagons
Min Yan
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combina…
Spherical Tiling by 12 Congruent Pentagons
Honghao Gao, Nan Shi, Min Yan
The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is kno…