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

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.