Hi everyone, I've lurked here occasionally but this is my first post.

I've been playing around with split-quaternions, and I'm particularly interested in a certain subset of them, restricted to a region bounded by a curious 4d shape I now know (from searching the forum) is called a "bicircular tegum". (If anyone's interested, I got here from the 2d split-complex numbers, in which the corresponding region is a square, which I guess would be a "bilinear tegum"?)

I've managed to work out that its hypervolume is (pi^2/6) r^4, one third that of a glome. But I need to know its surface volume too, and I thought I'd ask here before breaking out the integrals.