I had grand plans for this puzzle, and while it didn't turn out 100%, the results were reasonable. Carter made the first version of this that I ever saw although an indistinguishable picture was on Hendrick's site for years. Carter made it with a build-up of milliput whereas, mine involved preparing a Seventowns 2x2x2 cube, making pyramid sections and gluing these on. The only glitch was the fact that the cubies on the Seventowns 2x2x2 are not perfectly cubic.
This is not a problem for the average user, but it meant that my puzzle didn't work 100%. Anyway, read on.
Creating the Pyramids
I started with a print-out of a small triangle where three meeting would make a small pyramid. I glued these to pieces of phone card, and when it was dry, used a very sharp knife and steel edge to scour the cutouts. Then I ran the knife down these outlines until the triangles cut out.
I used small strips of tape on the outside of the triangles to hold them together temporarily, and then placed strips of milliput inside the pyramids as a more permanent method of gluing the together. I let this dry overnight.
Once that was secure, I removed the tape from the outside of the pyramid and placed more milliput on the outside of the pyramid where the triangles join. Again, this was left overnight.
Next day, I used fine sandpaper to rub each triangle flat again. This formed nice sharp edges and a perfect pyramid. I had a choice here to either leave it as it was, or round the dividing lines between the triangles. I left it as it was.
I made a mold of the pyramid, in two halves and cast up 8 black pyramid pieces, or covers, as that's what they really are.
Making the Core
This part is relatively simple. Take a 2x2x2, remove the stickers and shave a flat area on each edge. This helped in positioning the pyramid covers and gave a greater surface area to bond the pieces.
I used blobs of milliput to anchor the pyramids on the 2x2x2 cubie corners. This is a good method as it allows you to align all the pieces which can be very time consuming. It is best if you only do 2 or three pieces a day, as once all the pices are on and are floating on blobs of milliput, there will be nothing stable to compare against. And you will need to shuffle the puzzle to check alignment.
As I mentioned before, I used a Seventowns 2x2x2 which is not 100% in porportion. Not enough to be noticed usually, but when you are working with a modification, the differences cause gaps and sometimes overlapping of the pyramids. So getting it right took some time.
Once you have all the pieces on and all the milliput is dry, expect a piece to fall off here and there while you manipulate the puzzle. In fact, it's best to try and get each of the eight pieces to fall off. Milliput does not bond well to a shiny polyethelene surface. Once a piece falls off, superglue it back on in the EXACT ORIENTATION!
Once all that was all done, I made up some stickers and the 2x2x2 Rhombic dodecahedron was finished. I will be remaking it again, but next time, I will use either an Eastsheen 2x2x2 cube or a 2x2x2 puzzleball. Both of these are technically correct in all dimensions, and as the pyramid master was carefully built to be 100% correct, it should look great on a perfect 2x2x2 core base.