A Klein bottle is a mathematical object, "an example of a non-orientable surface". A bottle that has no 'inside' or 'outside', because the 'inside' is continuous with its 'outside'. The only way to represent a Klein bottle in a three-dimensional space is by allowing the surface to intersect itself. This would not be needed if we were using a four-dimensional space but, alas, we're not specially good at visualizing surfaces immersed in four-dimensional spaces.
By carefully chosing the representation, a Klein bottle can also be a very beautiful object. Condensation Land features one: you can find it floating on top of the Condensation Land Club, Classical Dance floor.
Apart from being beautiful, the bottle has some interesting Opensim-related properties. They are listed in the above video, and explained in detail in this blog post, where you'll also find the recipe (i.e., the LSL scripts) needed to create your own.
It's also an example of an Opensim-only object: it consists of a huge number of prims (2889, to be precise), that cannot be linked together in Second Life, while they are able to in Opensim.
The bottle was first created in Condensation/SL on august 2008; of course it could not rotate, because it couldn't be linked as a single object, but nevertheless we had a lot of fun with it (maybe I should have said 'inside' it :)).
One year later (july 2009) it was successfully migrated to Condensation/Opensim, where I was able to link it into a single linkset and therefore rotate it.
The 2889 prims glowing rotating Klein bottle can be visited from the Hypergrid by teleporting to Condensation Land in the Metropolis Grid. You will find a teleporter to a nice viewpoint for the bottle in the arrival point.
Update 20160825: Plastichansa Bade has kindly produced a mesh version of the Klein bottle, undistinguishable from the original one. The whole structure has now an impact on the parcel of only 2, versus 2889. Thank you!