Klein Fläche

grabcad

The Klein Fläche is often referred to as the Klein bottle, a strange mathematical anomaly comprised of two Möbius surfaces. Though it may not be as well-known as Möbius' monster, I believe it's far more intriguing. When searching online, you can find artisans who have successfully crafted one from glass - hand-blown. Its practical applications extend beyond its unusual appearance; for instance, you could fill it with a sweet treat and suspend it upside-down in the garden, where it would function perfectly as an artistic flycatcher! Similar to my previous encounter with the Möbius surface, I encountered difficulties when attempting to combine Rhino into a single surface. Like the Möbius surface, the surface direction is flipped, and where the surface requires attachment to itself, its direction is opposite. To clarify this complex concept, I've included a screenshot. I deliberately left the "hole" closed by the intersecting piece of surface to ensure mathematical accuracy. However, the attachment problem lies at the blend on the rim of the hole. If you try to remove the blocking piece of surface, you'll find it challenging without reconstructing the entire bottle.