 The chain is closed, meaning that every sphere in the chain has two tangent neighbors; in particular, the initial and final spheres, "S"1 and "S"6, are tangent to one another.The annular Soddy's hexlet is a special case (Figure 2), in which the three mutually tangent spheres consist of a single sphere of radius "r" (blue) sandwiched between two parallel planes (green) separated by a perpendicular distance 2"r".In this case, Soddy's hexlet consists of six spheres of radius "r" packed like ball bearings around the central sphere and likewise sandwiched.