An improved acetabular cup prosthesis has a cup body with inner convex and outer concave surfaces. The cup body has an apex and a base that defines a plane. The cup body outer convex surface has a toroidally shaped portion between the base and the transition. In one embodiment, the outer convex surface is toroidally shaped between the rim and a distance about one third of the distance of the rim to the apex. In another embodiment, a plurality of cup bodies are provided in a range of sizes between about 40 mm and 80 mm. Each cup body has a companion rotary reamer that is correspondingly shaped. The companion cup body is oversized between about 1 mm and 3 mm so that a generally constant change in volume is provided for all cup sizes between 40 mm and 80 mm.