An apparatus for mounting an object precisely in a specific plane. An object is mounted on small support points rather than flat pads or other flat surfaces. The support points are stiff but not completely rigid. Exactly four support points are used. Mechanical forces are sufficient to slightly compress the two higher support points on a diagonal and to slightly compress the object so that the object presses against all the support points, with a higher amount of compression for one pair of diagonal points relative to the other two points. In an example embodiment, the support points are formed at the intersection of curved surfaces or at the intersection of multiple planar surfaces. In a specific example embodiment, the points are formed at the intersection of cylindrical surfaces. The points are fabricated by a cylindrical cutting bit that has partial-cylinder grooves formed circumferentially in the bit. The outer surface of the bit is used to mill two intersecting planes, and the grooves result in cylindrical surfaces intersecting at the same angle as the intersecting planes. The resulting support points are true singular points, but with limited compressibility because of the shallow angle of the material just below the points.