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I recently saw or read somewhere of a group of geometrical bodies that share a special property with the sphere: no matter how you rotate them, they have the same "thickness" in all directions. They had a specific name. Does anyone know what I'm referring to?

Thanks!

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Or maybe better: en.wikipedia.org/wiki/Surface_of_constant_width. Or just type "constant width" into Google; many links appear. –  Gerry Myerson May 11 '12 at 3:43

1 Answer 1

Perhaps you mean spheroforms? enter image description here

In a two dimensional plane it is Reuleaux triangle.

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If you're British, take a hard look at a 50p coin. It has to have constant diameter so that it will work in vending machines, I suppose. There's also an interesting drill bit that can be used for drilling square holes (whose name I have long since forgotten). –  bubba May 22 '12 at 15:34

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