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Tilings of the Sphere by Congruent Pentagons IV: Edge Combination $a^4b$

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

Hoi Ping Luk , Min Yan This is my paper · ORCID
classification math.COmath.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 4 Pith papers

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

  1. Non-side-to-side tilings of the sphere by congruent triangles with any irrational angle

    math.CO 2025-05 conditional novelty 8.0 of 10

    Any non-side-to-side spherical tiling by congruent triangles with an irrational angle is either a 2-layer earth map tiling, an 8-tile family, or the unique 16-tile sporadic tiling.

  2. Dihedral Tilings of the Sphere by Kites and Regular Polygons

    math.CO 2026-07 accept novelty 7.0 of 10

    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.

  3. Tilings of the sphere by congruent pentagons V: Edge combination $a^{4}b$ with rational angles

    math.CO 2025-07 conditional novelty 5.0 of 10

    Rational-angle a^4b pentagonal sphere tilings are exactly three families: a 12-tile tetrahedral subdivision, a 4m-tile symmetric family with flips, and a 20-tile non-symmetric case.

  4. Tilings of the sphere by congruent pentagons IV: Edge combination $a^4b$ with general angles

    math.CO 2024-12 conditional novelty 5.0 of 10

    All sphere tilings by congruent pentagons with edge pattern a^4b and at least one irrational angle are classified as three 1-parameter subdivision families and a sequence of 3-layer earth-map families.

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