A long time ago I created a 3d-printed Klein bottle for my own amusement. What’s a Klein bottle? A Klein bottle is, simply put, a non-orientable, manifold object. Now, you could go look up the Wikipedia article about Klein bottles (and I suggest that you do, they’re really cool) but the most important thing to note is that a true Klein bottle could only exist in 4-dimensional space. But you just said that you 3d-printed one! Well, yes, I did say that. But my statement wasn’t quite accurate. What I had 3d-printed was a 3-dimensional representation of a Klein bottle. Basically I used the object’s boundary as the basis for creating a shell, from which new 3-dimensional boundaries were defined. By offsetting certain points along the bottle before defining the shell, I could create a 3d object from what was once a 4d object. Pretty cool, right?
This is by far my favorite 3d-printed object, at least of the ones I’ve made so far. I have always found mathematical objects fascinating and while I have printed a multitude of Möbius strips in various styles, something about this Klein bottle makes it seem so unique and mysterious that I can’t help but pick it up and fiddle with it all the time.
If you’d like to get your very own Klein bottle (and I assure you that you do) then you can buy them from my Shapeways store here.