Klein Bottle Design with Solidworks

grabcad

Klein bottle, just like the more familiar sphere, is a closed surface: it's finite in the sense that you can fit it into a finite region of space, but an ant could walk around on it forever without ever encountering a boundary or falling over an edge. Unlike the sphere, which has an inside and an outside, the Klein bottle is one-sided: walking around, our ant could reach both sides of each point of the surface. This is why the bottle encloses no volume, and it also answers the "why" question: the Klein bottle is interesting because we don't encounter many one-sided shapes in nature.