Klein bottle bottle opener (Bottle Opener)

Take your binge drinking to the same dimension!

This immersion of the Klein bottle in 3D space has a modified bottom which acts as a bottle opener. The cutouts on its surface allow a view of its self-intersection while keeping the model easy to print and contributing to its overall organic shape.

The Klein bottle is non-orientable, closed, and has no boundary. It lives in 4D space, but we visualize it as an immersion in 3D space. Its non-orientability means an object moving along this surface ends up at its starting point flipped upside-down and mirrored. It was first described by Felix Klein in 1882.

More information on the Klein bottle:

Imaging maths - Inside the Klein bottle | plus.maths.org (archive.org)

Instructions

Prints at 0.15 mm layer height without supports. Use a tough material like PLA+, otherwise it might break (and depending on how it breaks, it might instantly become orientable!). Infill percentage is not important, just make sure the opener part is printed in solid infill.