I'll start with a complaint about the Tetratorus. First, I still think it should be called a tritorus or a 3-torus, but I'll wait for Rob to come back before we argue about that.

The other thing is the surcell volume and bulk. I changed it from 4pi R r to 4pi R r a, and someone changed it back saying

Trust me, it isn't multiplied by a - there's a complex formula that cancels it out.

Who said that, and what's this complex formula that somehow gives you a volume measured in square meters?

Anyway, I've just calculated the integral directly with mathematica, and I get:

V = 8 pi^3 a r R

B = 4 pi^3 a^2 r R

So it turns out we were both wrong.