An attempt was made to offset or shell patch P0, and gyroid boundary patch.

It appears that the "symmetry" operations have resulted in Flip of some surface normals, as some patches offset or shell in opposite directions.
Also P1 and P2 offset or shell with a little wiggle near a corner.

PatchPO Shell Centerline, 0.02, works very well. Node creation from PatchPO Shell slolid to the boundary patch with 12 solids looks good.
Boolean union two of the 12 solid patches has not worked. But hiding two skins and deleting the two surfaces in common, does permit two solid patches to boolean.

A few stray curve segments were created a some time...

- Brian

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...