Soddy's hexlet

Chain of 6 spheres tangent to 3 given spheres

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, the three spheres are the red inner sphere and two spheres above and below the plane the centers of the hexlet spheres lie on. In addition, the hexlet spheres are tangent to a fourth sphere, which is not tangent to the three others.

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