The above image lets you see the
interior central rhombic dodecahedral cell in the size-five
tetrahedron. It also indicates how the tetrahedron and octahedron
can combine, e.g., to make a stella octangula.
The idea for this construction comes from a paper titled "Satterfield's
Tomb" by David Klarner and Wade Satterfield (edited by Thane Plambeck)
in the book
A LifeTime of Puzzles:
Honoring Martin Gardner,
edited by Erik Demaine, Martin Demaine and Tom Rodgers. However,
I am using a slightly different set of cutting planes than what is
described there. (They propose only the regular tetrahedron and
choose its planes as tangent to the spheres which inscribe the rhombic
dodecahedra. I chose a parallel set of planes with "natural" integer
intercepts, so one shape of face cells can be used in both the
tetrahedron and the analogous octahedron.)
The cells above are made of nylon on a selective laser sintering
machine. To minimize materials, I scaled these parts to be about 0.5
inches across, so they look like fancy sugar cubes. That works
for me, as these images show, but you
might prefer larger units for ease of handling.
If you have any kind of rapid prototyping machine, you can make your
own cells by using these stl files: