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.
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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.
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 :)
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.
There are lots of projects that do this (implement a Klein bottle with a crossing).
Even my dad has knit several Klein bottle hats for fun, inspired by one of those projects. I got one as a Christmas present.