Wormhole Platonic Polyhedra

If a really smart worm tried to communicate its understanding of Platonic polyhedra to you, this is what your apples would look like.

These shapes were created by projecting the faces of the five Platonic polyhedra on to a sphere and then connecting pairs of faces with internal tunnels.

There are multiple possible configurations of tunnels possible with the octahedron, dodecahedron and icosahedron, but many of them result in horizontal internal surfaces which would be problematic for printing. There is enough vertical component in these orientations that support is only needed around the base.

The pictures above show the tetrahedron, cube and octahedron. Files for the dodecahedron and icosahedron are also included.

The measurement on each file is the approximate sphere diameter.