The 600-Cell

I can’t stop thinking about the 600-cell:

It’s a ‘Platonic solid in 4 dimensions’ with 600 tetrahedral faces and 120 vertices. One reason I like it is that you can think of these vertices as forming a group: a double cover of the rotational symmetry group of the icosahedron. Another reason is that it’s a halfway house between the icosahedron and the lattice. I explained all this in my last post here:

• From the icosahedron to E8.

I wrote that post as a spinoff of an article I was writing fo...