In geometry, Soddy's hexlet is a chain of six spheres (shown in grey in Figure 1), 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 (not shown) above and below the plane the centers of the hexlet spheres lie on. In addition, the hexlet spheres are tangent to a fourth sphere (the blue outer sphere in Figure 1), which is not tangent to the three others.