The 12 patches of the boundary surface do not quite meet at the center. Some faint grooves are visible in the resulting surface. Boolean union of the shelled patches created up to 3 each of sliver solids that look like lines... The python math is not perfect... Join was an alternative to Boolean union, also showing the 'grooves".
The project is probably sufficiently complete to move on...
Or further investigate the papers math for z coordinates...
And investigate the symmetry "Flips"...

- Brian

Boolean union once created or modified two offset surfaces which acted as one surface, and also sometimes deleted one surface...