A golf ball is disclosed having a plurality of dimples on its surface, the dimples being arranged in patterns determined by the science of phyllotaxis. Phyllotactic patterns are used to ascertain the placement of dimples in each polygonal face of a polyhedron based dimple pattern. Phyllotactic patterns provide for the arrangement of multiple spiral shaped strings of dimples within individual polygonal faces of a golf ball surface, with each polygonal face area having its own phyllotactic origination point at its center. The resulting multiple axes of symmetry in the overall dimple pattern provide improved symmetry of flight performance.