I made this torus with cardstock and a lot of patience. Its made entirely out of many copies of this template, cut out of cardstock. I used a papercutter machine to cut the paper, but scissors should work fine.

The torus is constructed out of two spirals, one green and one red, one rotating clockwise and the other counterclockwise. These weave between one another, interfacing using the provided notches.

I kept adding layers until I could comfertably wrap the stack around into a circle. It took about 50 layers of each color. Here’s what the accordian looks like all compressed.

The final torus is fun to hold because it rotates around its axis very well. If you just grab the outside, it can wriggle from your grasp like one of those water tube toys.

This one is made out of corrougated paper, and is similar in design to mine. It’s heald together by magnets, so it can freely switch from torus mode to straight mode. I bought this online, sold as a cat toy (specifically this one). Highly reccomend.

I spun this one on a potters wheel (a tool designed specifically for surfaces of revolution). I still haven’t fired it, fingers crossed that it will survive the endevor.

A bracelet I found in the thrift store. It’s made of 100 metal rings, each interlocking with every other ring. Topologically, the rings are all fibers of the Hopf fibration. If you hold all the rings together, they form a filled torus.

Successful paper torus, woven out of many circles. This weaving pattern is not topopolgically regular. The blank spaces on the inside and outside of the wheel are 4-sided, while on the front and back they are only 2 sided. Also, the paper doesn’t conform to the surface of the torus like one might want. Still, its nice and quite studry. This is the prototype for the PVC construction of the skeleton of my Halloween costume, see next picture.

This is the skeleton of my horuse costume. This torus is made of PVC wrapped into tubes, woven into one-another. It’s very sturdy, and can roll around like a wheel. I’m very proud.