All edge-to-edge dihedral spherical tilings by kites and regular m-gons (m≥4) are classified into earth-map, Platonic, and Johnson-Zalgaller types with explicit AVCs and constructions.
Tilings of the Sphere by Congruent Pentagons IV: Edge Combination $a^4b$
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
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 edge-to-edge tilings of the sphere by congruent equilateral pentagons of other types, and our classification of edge-to-edge tilings of the sphere by congruent quadrilaterals or triangles, we complete the classification of edge-to-edge tilings of the sphere by congruent polygons.
fields
math.CO 3representative citing papers
An algorithm enumerates all tilings of negative-Euler-characteristic surfaces by n-gons (n≥7) with fixed tile count, with explicit two-tile computations on small-genus surfaces and analysis of edge lengths.
Investigates edge-to-edge spherical tilings by angle-congruent pentagons and the impact of reducing angle distinctions.
citing papers explorer
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Dihedral Tilings of the Sphere by Kites and Regular Polygons
All edge-to-edge dihedral spherical tilings by kites and regular m-gons (m≥4) are classified into earth-map, Platonic, and Johnson-Zalgaller types with explicit AVCs and constructions.
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Tiling of Hyperbolic Surface by Multiple Tiles
An algorithm enumerates all tilings of negative-Euler-characteristic surfaces by n-gons (n≥7) with fixed tile count, with explicit two-tile computations on small-genus surfaces and analysis of edge lengths.
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Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons
Investigates edge-to-edge spherical tilings by angle-congruent pentagons and the impact of reducing angle distinctions.