Originally published at: https://boingboing.net/2020/01/10/watch-these-cool-sphericons-ro.html
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I once made one of the equilateral triangle ones on my wood lathe. I wood-glued 2 pieces of wood together with a piece of paper bag in between, which gave a bond that was strong enough for turning, but then easy enough to split afterwards. I turned the cone and then split the pieces, cleaned up the faces, rotated, glued, sanded, and finished. IIRC, I made a hollow in the center and added a couple hex nuts during glue-up to add some heft.
It was a relatively straightforward and fun project and yielded an intriguing and satisfying object. I think I gave that one to my dad. I kinda want to try one of the more complicated ones now (the equilateral cone was easy for a woodturning novice because as long as you’ve got straight edges and keep the angle from the base to the side correct, you can’t really screw up the shape).
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If they were doing a The Prisoner remake, use one of these for Rover’s ground motion.
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Two words: Cat Toy.
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Not sure what’s so awesome about a drunk wheel.
(I kid, I kid - it’s really cool!)
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re the cone rolling, the presenter says: “It can’t continuously roll, it just stops. And this is true for all odd-sided permutations.” 
Yet he provides no proof… I would think this would be feasible to prove…
This is going to bug me.
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Agreed. Neither can a sphere or wheel on a level flat surface, due to friction. It certainly looks like the spheroids would keep up with an equivalent wheel.
Ah, I found a site enumerating the variations and the statement would appear to be true as follows. The sphericons start as polygons rotated about an axis. With polygons of odd-numbered sides that rotation generates a “flat” circle at the bottom. That leaves the rotations inevitably ending up at some point on a flat spot made up of a semicircle.
I’m sure you could write all of this as a group, but I’m happy with that answer. 
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Those were really wacky, and really cool. 
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