An MRI rf coil array is comprised of a large number of separate coil elements that are supported on a substrate that is shaped to the contour of the anatomy being imaged. The coil elements overlap each other to reduce mutual inductance and their location is determined by tiling the surface of the substrate with regular, substantially same sized polygons. The center of each coil element is aligned with the center of a polygon. By using a mixture of different polygons, such as hexagons and pentagons, an arrangement of coil elements may be formed that cover a surface with non-zero Gaussian curvature where each coil is overlapped with its neighbors such that their mutual inductance is nulled.