[tempodox]

This would be even more awesome if the puzzle pieces were curved, so they'd form a Klein bottle when put together.

[mcherm]

That would be INCREDIBLY awesome, considering that it would require pieces that have a curve in to the 4th dimension (or perhaps just pieces that could pass through each other). A Klein bottle is a 2-dimensional surface cannot be embedded in a 3-dimensional space without crossing.

[tempodox]

While this is true mathematically, there is at least one project that emulates Klein bottles in 3D quite credibly:

http://www.kleinbottle.com

Edit: You can even put in some liquid (the “hose” continues through the crossing). The fun part is getting it out again :)

[emmelaich]

Hey that's the famous Clifford Stoll of Cuckoo's Egg fame.

Glad he is not famous only for that book. As fine as it is.

[mcherm]

There are lots of projects that do this (implement a Klein bottle with a crossing).

[dancek]

Even my dad has knit several Klein bottle hats for fun, inspired by one of those projects. I got one as a Christmas present.

[p1mrx]

I think the flat version is a more authentic representation of the 4-dimensional object. If you were a 2D creature embedded in the surface of a Klein bottle, space would seem flat in every direction... at least until you went out for a walk and found the mirror-image of your house.

[askvictor]

I have a 3D jigsaw puzzle that makes a globe (i.e. the Earth) that consists of curved plastic pieces. It shouldn't be too hard to make such a Klein puzzle, though solving it is harder. The globe puzzle includes a small bowl (of the same radius as the finished globe) to assist putting the pieces together; this wouldn't be possible with a klein bottle due to there not being a consistent radius.