High Quality Content by WIKIPEDIA articles! In geometry, Soddy's hexlet is a chain of six spheres, each of which is tangent to both of its neighbors and also to three mutually tangent given spheres. In Figure 1, these three spheres are shown as an outer circumscribing sphere C (blue), and two spheres A and B (green) above and below the plane of their centers. In addition, the hexlet spheres are tangent to a fourth sphere D (red 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; in this, Soddy's hexlet is the spherical analog of a Steiner chain of six circles.

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