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A Klein Bottle is a surface with one side, like a Möbius strip made more 3-dimensional.  It looks as if it's about to enclose some space like a regular bottle, then it curves back on itself with a twist, so the inner side of the bottle merges with the outer.  Then suddenly it doesn't enclose any volume at all: the inside and outside spaces become one.

Discovered in 1882 by Felix Klein, the Klein Bottle has been a fascinating trick of space ever since.  It can't quite exist in 3D, the surface has to cross itself to make the twist possible, but we can still make amusing models that show how it works.

This one is 3D printed in durable, washable stainless steel.  It's sized to fit the hand sweetly.  It's the perfect finishing touch for any math fan's kitchen, and you don't have to know geometry to enjoy it.

Yes, it really opens bottles!
 

Klein Bottle Opener  3" tall - $72

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Perhaps of historical interest: the first version of this page.  I might have opened one bottle too many before I wrote it.

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