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<p>We develop a systematic method for deriving the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method provides an effective and necessary tool in solving many tiling problems about pentagonal tilings of the sphere. More significantly, we determine all the angle combinations that allow free and continuous choices of two angle values.</p>

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Angle Combinations in Tilings of the Sphere by Angle Congruent Pentagons

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月31日

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  • Hoi Ping Luk,
  • Min Yan

摘要

We develop a systematic method for deriving the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method provides an effective and necessary tool in solving many tiling problems about pentagonal tilings of the sphere. More significantly, we determine all the angle combinations that allow free and continuous choices of two angle values.