Animation showing the family of solutions to the problem of Soddy's hexlet, a three-dimensional analog of the Steiner chain.  The six grey spheres are always tangent to both the inner red sphere and to the outer blue sphere, and also to their two neighbouring grey spheres.  These spheres always touch on their equators.  The equator of the outer blue sphere is highlighted in gold.  Not shown are two additional spheres, above and below the red sphere, to which the grey spheres are always tangent.
<a href="//commons.wikimedia.org/wiki/User:WillowW" title="User:WillowW">WillowW</a>
CC BY-SA 3.0
<span class="int-own-work" lang="en">Own work</span>