Dihedral tilings of the sphere by regular polygons and quadrilaterals I: squares and rhombi

September 12, 2025Combinatorial TheoryOpen Access

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Key Points

The study categorizes how squares and rhombi can tile the sphere through edge-to-edge dihedral methods, enhancing mathematical understanding.
Key findings support the classification of spherical tilings, showcasing relationships between squares and rhombi in complex geometric formations.
A developed method for edge-to-edge dihedral tilings may facilitate analysis of additional mathematical tiling problems in future research.
The study's implications call for expanding the classification techniques to include other types of polygons and space divisions.

This classification reveals edge-to-edge dihedral tilings in spheres using squares and rhombi, suggesting future applications.

We classify the edge-to-edge dihedral tilings of the sphere by squares and rhombi and develop a method that can be applied to future problems.

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Hoi Ping Luk (2025) studied this question.

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