 In addition, the hexlet spheres are tangent to a fourth sphere (blue in Figure 1), which is not tangent to the three others.According to a theorem published by Frederick Soddy in 1937, it is always possible to find a hexlet for any choice of mutually tangent spheres "A", "B" and "C".Indeed, there is an infinite family of hexlets related by rotation and scaling of the hexlet spheres (Figure 1); in this, Soddy's hexlet is the spherical analog of a Steiner chain of six circles.