This invention refers to the structure for a ball or ball cover that comprises a plurality of interconnected panels comprising first and second groups of panels which combined form a sphere. The first group of panels define at least two different surface areas of the ball or ball cover disposed at polar extremes on the surface of the sphere and the second group of panels define an area of the surface in the form of a ring, with at least three undulations and disposed in the equatorial zone of the surface of the ball or ball cover, creating a separation between the polar extremes defined by the first group of panels; whereby the width of the ring is modified to improve the sphericity of the ball or ball cover and obtaining a ball of a selected measurement (C).