 An infinite variety of hexlets may be generated by rotating the six balls "s"1–"s"6 in their plane by an arbitrary angle before re-inverting them.The envelope produced by such rotations is the torus that surrounds the sphere "c" and is sandwiched between the two planes "a" and "b"; thus, the torus has an inner radius "r" and outer radius 3"r".After the re-inversion, this torus becomes a Dupin cyclide (Figure 3).