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arxiv: 2307.11453 · v3 · pith:D7A3PTHB · submitted 2023-07-21 · math.CO · math.MG

Tilings of the Sphere by Congruent Pentagons IV: Edge Combination a⁴b

Hoi Ping Luk , Min Yan This is my paper

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classification math.CO math.MG
keywords congruentspheretilingsedge-to-edgepentagonsclassificationequilateralalmost
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Tiling of Hyperbolic Surface by Multiple Tiles

    math.CO 2026-04 unverdicted novelty 5.0

    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.

  2. Edge-to-edge Tilings of the Sphere by Angle Congruent Pentagons

    math.CO 2025-10 unverdicted novelty 5.0

    Investigates edge-to-edge spherical tilings by angle-congruent pentagons and the impact of reducing angle distinctions.