Above is a gif of an interactive model of hyperbolic space tiled with 12 Days Dodecahedra. It’s part music video, part mathematical model, and all holiday cheer (or absolutely terrifying, depending on who you ask).

At this point it seems obvious to me that one must tile hyperbolic space with right angle dodecahedra that have pictures of gifts from a holiday song that blink on and off in time to a 12-tone rendition of the music, and that it should be accompanied by a holiday craft so you can make your own dodecaration (hyperbolic space not included).


Equally obvious is that it should be in virtual reality. The interactive page is webVR-enabled, so if you’ve got a webVR browser and a compatible headset you can navigate through the hyperbolic space and see the interesting stereo effects. It’s cool in a regular browser, and it’s REALLY cool in VR. It’s like hyperbolic space is what VR was made for.

There’s also a video version if you like. The comments are interesting. Most people associate dissonance with horror films, and most people aren’t familiar with the strange curvature of hyperbolic space, so I guess I understand why it’s frightening to some people, despite the ridiculous graphics. Looks normal to me…

The song and craft page are both public domain (CC0), so feel free to do whatever you like with them! You can download the original Illustrator file, pdf, or jpg.

The interactive code stuff comes from a massive collaboration with Henry Segerman, Andrea Hawksley, Mike Stay, Marc ten Bosch, and draws from code by many others. The whole open-source mess is on github.

For more 12 days math fun, see the Gauss Christmath Special:

and for a better understanding of 12-tone music, see Twelve Tones:

In theory I’d like to talk more about this whole project, but I’ve got more twelve tone carols to make!

edit: here’s one!

edit2: here’s another!

Also another interactive holiday thing, “child.