Wireframe Klein Bottle inside glass Klein Bottle

Here is a peek at something in the works as an animation, I thought it would be neat to get a “3D printed” wireframe bottle inside a glass bottle.   I gave this model a twist in both the mesh and in the overall geometry to increase the curvature and break the bilateral symmetry of most bottles.


Feel free to leave a comment below!


Virtual Klein Bottles

Welcome to my virtual Klein Bottle gallery! Recently I have become interested in Klein bottles and am starting this site as a gallery for virtual Klein Bottle inspired art.

So, what is a Klein Bottle, you ask?

From Wikipedia, the free encyclopedia

In mathematics, the Klein bottle/ˈkln/ is an example of a non-orientablesurface; it is a two-dimensionalmanifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include theMöbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).

The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It may have been originally named the Kleinsche Fläche (“Klein surface”) and then misinterpreted as Kleinsche Flasche (“Klein bottle”), which ultimately led to the adoption of this term in the German language as well.

Read more about Klein bottles on Wikipedia

The unique manifold topology  and the edgeless, boundless form lends itself well to making beautiful forms, both mathematically and aesthetically.   Here are a few images to get started, these are all 3D models in virtual space only, none of these are physical objects.

This is just the beginning, an experiment intended to explore the intersection between science, art, and materials.   In the future i will be creating many more still and animated works based on the topology in the context of minimalism and surrealism.

Are you excited about Klein bottles or other wonders of topology too?   Tell me all about it in the comments section!

A virtual Klein Bottle gallery