The idea of these is not that special. I guess I'm not the first who had the idea of building these. The idea is a 3D extension of Sierpinky's Sieve. The number of faces increases rapidly; the first one has 8x6=48 faces, the second phase 6 times as much, and the 3rd phase 8x6x6x6=1720 faces!
It took me something like 1 month to build this last one; though I was only building in the evenings. Sometimes people ask me if I am planning to build the next phase. No way! Not only, because keeping the same size will be almost impossible, but also because that one will take me like a half year, and as a result people will probably still ask me the same question. :o)
If you're interested in building these I prepared a PDF file. Just download and print it on a colour printer.
To build the first one, you need to build 6 octahedra and glue them together by their edges. This seems perhaps a little bit difficult, but is in fact quite easy. The 8 octahedra should be build from the first page. There are 4 spares on this page. By the way, I cut of half of the tabs.
For the second phase you'll need to build 36 octahedra. These can be found on page 2, which includes 4 spares. Out of these 36 octahedra I built 6 small models of the first phase and glued those together.
For the third one you'll need to build 216 octahedra. The 3rd and the 4th page should be sufficient. Again I built that one by building 6 of the former phase.
Good luck, and let me know if you have questions or when you succeeded!