Fun with twisted toruses (or tori, if you must)

 Upload 2010 08 Math Monday The Twisted Torus Ambrasobject

 Upload 2010 08 Math Monday The Twisted Torus Torzle-Part

George Hart of Make: Online says, "A twisted torus is a donut which twists as it closes on itself." Besides making me hungry for a Krispy Kreme, this twisted torus makes me want to ask one of my MakerBot-owning pals to print out a bunch of parts so I can try to build one myself. How do you close the loop?

[Above] is an elegant solution from the 16th century: a twisted torus in the Schloss Ambras Museum, assembled from seventy-six identical wood components.

Each piece has a slot for the next to pass through and there is enough play in the slots for the chain to be twisted slightly before closing into a loop. It is a visual puzzle to figure out how the ring was closed. If you make many copies of the basic unit sketched below, you can try to solve the puzzle and assemble them into your own twisted torus.

Math Monday: The twisted torus