Attached is a spheroform uniform width, symmetric tetrahedroid. [See next post for update.]
Despite being very careful, somehow the corners get out of wack. So the model does not appear to be quite perfect.
There seems to be a problem with a very slight lack of symmetry with maybe the circular array command, or something.

The canal surface "wedges" were made with loft of only 21 numpoints.

Using a Vee trimming tool object on the 4 master spheres, and the wedges, enabled the joining of the parts.

A script which arrays objects in a tetrahedral layout would be helpful.

- Brian.

A cleaner version of the uniform width, symmetric spheroform tetrahedron, starting with the 4 corner points of a tetrahedron of edge-length 2√2 from wikipedia. Later scaling to edge-length 1. Trimming the 4 spheres was laborious, whereas previously it was near onestep. The orientationn of the spheres must matter a lot. Added one canal wedge trimmed with angle Vee. Lots of trimming. Used Orient Line/Line multiple times, which generally placed surfaces with correct orientation, without resorting to cplane.

- Brian