Musing the muses

I started a story the other day, which I think I might actually get to finish and send to a magazine or two. Unfortunately the muse of mathematics kicked in and I created a new image for my gallery. It's not bad, but it is a bit boring and doesn't cover any new ground. I thought I'd take the same concept and use a lattice based on other space-filling polyhedra. There are a few out there but I don't have the coordinates for them.

I thought that I would start with the truncated octahedron. Finding the points of the vertices has been a bitch. I first calculated the vertices for a cube and an octahedron and found the intersection of those two shapes. What I get isn't perfect, since all of the edges of the truncated octahedron are equal, and the vertices are all equidistant from the origin. I thought that if I found the points where the faces intersected and normalized those vectors I might have a shot at getting a proper shape. I've gone through several pages of notes, erasing or crossing off half of what I've done. I should just use Python to figure this stuff out. It's lazy and I'm ashamed to admit it, but I am.