#klein bottle

[dreams-of-soft-rain]

[thalescircles]

This is such a delightful opening paragraph for a paper.

(From “Surfaces with Klein bottle topology occur in fusion reactor fields” by C. B. Smiet. Shared with me by my father-in-law, who is a physicist.)

[more-mathematics-mor-lam]

Finally some poetry of interest to me

[noosphe-re]

The space that this male fiddler crab (a chiral object) lives in, a Möbius strip, is non-orientable. Note that the fiddler crab flips to being its own mirror image with every complete circulation (Non-orientable wormhole)

[oneefin]

best square gluing diagram shape

disc

annulus

möbius strip

sphere

torus

klein bottle

real projective plane

(show results)

Voting ended onSep 28, 2025

you know, the topology thing where you can pair up sides of a square or a rhombus or whatever and glue them together in a certain direction get a shape? and sometimes the shape only exists in 4 dimensions?

there's lots of sources online that list a subset of these options (like the wikipedia page for fundamental polygons), but i didn't see anything that had all 7 of these options listed, with diagrams, so i did it myself. i think it's exhaustive?

[mathhombre]

Nonorientable Magic

[fiaphobe]

this is a cat trying to drink out of a klein bottle

[cosmonautroger]

Klein Bottle