Ball trapped in a spiral cage

If M.C. Escher had owned fidget toys, he would have worn "One ring to rule the ball" as a pendant. A single, continuous line contains a small ball that makes orbit after mesmerizing orbit but cannot escape, always held down in four directions. Available in solid, durable stainless steel with optional antique bronze and gold plated finishes to fit any context, "One ring to rule the ball" now also includes a free rubber necklace so that you can confuse your mind any time the fancy strikes you! One customer echoes many others in saying, "I couldn't put it down. This thing is just too fun!"

Purchases by those gracious customers have now paid for the design time on this piece so it is available on a pay-what-you-want basis. Ordering from this page contributes 5$ towards continuing work such as the new, even more impossible "One ring to pwn the ball" (just released October 18th!) which can be found at http://www.shapeways.com/model/145172/one_ring_to_pwn_the_ball.html and the open-source "Ultimate Desk Toy" at http://www.shapeways.com/model/109166/ultimate_desk_toy.html . To download the original 3d file for your own use under a CC-BY license ( http://creativecommons.org/licenses/by/2.5/ca ) click "Download" at top right . To learn more about this design or other work from Terra Cotta, visit our website at http://www.terracottapf.com

Another projection of the 4-dimensional hypercube, this one close to vertex-centered. I love the shape of its hull: almost a rhombic dodecahedron, but skewed just enough to keep the central vertices from meeting.
The more usual projection is here, other polytopes are here.

A four-dimensional cube at pendant size.  Is it adorable?  Why yes, it is. Some feel it is a little large to wear as jewelry, so I've uploaded a smaller one here.

More polytopes are here.