During the 2020 lockdown, I learned how to crochet. My initial goal was to crochet a sweater. To practice, I crocheted small things, like hats. After crocheting a dozen hats, I realized I had too many hats. I then started crocheting amigurumi (small stuffed creatures) following online patterns. I soon realized I could crochet mathematical surfaces. I designed my own patterns to create the following mathematical surfaces. I hope to one day present this in a more structured and educational way for people who want to crochet their own surfaces.

Klein bottle

As always, it began with a Klein bottle.

double Klein bottle

This is a double Klein bottle, which ends up just being a complicated looking torus.

Klein bottle figure 8 immersion

Here is another immersion of the Klein bottle known as the figure 8 immersion.

Boy's surface

Here is an immersion of the real projective plane into 3-dimensional space, known as Boy's surface.

Another immersion of $\mathbb R \mathbb P ^2$

Here is another immersion of the real projective plane. Here I crocheted a Mobius loop. Then crocheted a disc to the boundary. This eventually led to an issue (self-intersection), and the resulting object is a little hard to understand.

Bolza surface

Here is the Bolza surface.

Bolza surface unstitched

Here we see how the Bolza surface is constructed. First a disc is made. Then the boundary is broken into 8 segments, and colored as above. Then common colors are stitched together.