Thank you for all the kind words.
Solving is indeed equivalent to a Super Rex Cube.
@Claus: It is only fair to be asked such a question since I ask it quite often.
It weighs 390 grams compared with 144 for the original Rex Cube.
Edge length = 37mm
This puzzle was made by extending only. The red-blue-yellow corner you can see the in the first image is an "original corner" of the rex cube.
It was indeed very hard to make these round pieces. I did what I have done on other transformations: I stuff hard paper into the gaps, filled the spaces with Apoxie sculpt, removed the paper after hardening and then did a lot of sanding. Works great for a Pentagonal trapezohedron. Does not work that good for this one, sorry.
@Katsmom: Do you know what roxahedron is?