Universal mold frames for producing multi-piece golf balls are provided. The mold frames include lower and upper frame plates having locator pins that are inserted into corresponding locator slots in the mold cavities. The eccentric pin layout of the frame plates and corresponding slots in the cavities means the cavities can be fitted easily and aligned in the frame plates. The interior surfaces of the mold cavities define a specific dimple pattern such as icosahedron or tetrahedron-based patterns. The mold frames can accommodate cavities having different dimple patterns. A castable liquid polymer, for example, polyurethane is dispensed into the mold cavities, which are then pressed together to form the spherical cover for the ball.