 Inversion in the point of tangency between spheres "A" and "B" transforms them into parallel planes, which may be denoted as "a" and "b".Since sphere "C" is tangent to both "A" and "B" and does not pass through the center of inversion, "C" is transformed into another sphere "c" that is tangent to both planes; hence, "c" is sandwiched between the two planes "a" and "b".This is the annular Soddy's hexlet (Figure 2).