The 120-cell encodes the symmetries of the dodecahedron. This is probably my favorite mathematical surprise, and amazed and shocked me when I learned it (still amazes and shocks me). I always thought it'd be nice to write a blog post about this. This week, John Baez did a lovely post about this very thing, and I learned even more about the connection by reading it. He's been building up to that post with his #4d series. Here's a link to that series, which should hopefully filter out all the reshares you get by just searching on the hashtag. https://plus.google.com/u/0/s/%234d%20baez Originally shared by John Baez So here's the climax of the #4d story, though not the end. See this 'belt' of 60 dodecahedra that makes up half the 120-cell when you curl it up into a torus? Let's understand it! It might help if you first watch the 120-cell video again. So, what is this belt, and why is it made of 60 dodecahedra? First: each point in a ball of radius π descr
