The Binary Octahedral Group (Part 2)

Part 1 introduced the ‘binary octahedral group’. This time I just want to show you some more pictures related to this group. I’ll give just enough explanation to hint at what’s going on. For more details, check out this webpage:

• Greg Egan, Symmetries and the 24-cell.

Okay, here goes!

You can inscribe two regular tetrahedra in a cube:

Each tetrahedron has 4! = 24 symmetries permuting its 4 vertices.

The cube thus has 48 symmetries, twice as many. Half map each tetrahedron to itself, ...