Using Cross Product to make triangles...

Looking at the cross product, for triangle faces of a spherical polyhedron. I'm (mostly) making a honking big quad triangle pair at the back side of the volume and 'spherifying' the XYZ coordinates to the surface of the light blue sphere. I get two random points, derive a third point by subtracting p1 from p0 and adding that to p0 to get p2... and then get the third point as the cross product of the vectors from p0, all 'spherified'. The green triangle is p0-p1-p3 and the red is p0-p3-p2.
Whew! 8-P