Hi,
on the 3th of July Zhewei beat me in making the first dodecahedral shape transformation of cornerturning hexhaedron with 2 cuts per axis. By that time this puzzle had been sitting finished but unstickered on m table for two months. Sadly I can't proove that.
Now I present my Rexahedron to get a honorable 2nd prize. On the other hand: Zhewei took the easy road (?): He used a Master Skewb which was not available by the time I started this one. Therefore I used a Rex cube.
This puzzle does not change shape.
Enjoy.

Nice puzzle! How about an honorary first place tie?
The transformation of a Rex Cube is much harder, first off, the curved cuts are difficult to extend. I for one have no idea how to do this. Andreas, care to share your technique?

Awesome puzzle! I love how cubes like these look so crazy buy keep their shape.
This blows my mind.

Awesome!

Solving is equivalent to a "super" Rex Cube, right?

Very very good work!!!!!!!!!!!!

What about the size?
Do you need extension, or is this shape made with cuts only?

Wow nice one
How does the edge length? Thank.

Nice work Andreas. I love the curvy cuts!

Very nice. That looks like it must have been hard to make with the curved surfaces and all. Cool!

When can we expect to see the Roxahedon?

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?

errr....The crazy puzzle lady all squished and shoved down into a rather small space?

I have a feeling I will soon find out! Or maybe you will

I may be wrong here, but I cannot see where the smaller pieces are on this. Are they perhaps hidden underneath other pieces á la 3x3 -> 2x2? If they are not, where are they?

And if they are hidden underneath, does that affect the solving? I do not own a rex cube, so I do not know of any parities on it.

Oh, and as a side note- NICE! Where do you find the time needed to make such fantastic puzzles? I swear you have brought out a new one every week or less, and they are always so well made. You clearly have an abundance of creative talent .

I would tell you if there were something to tell. TomZ created the term Roxahedron. He is the one to blame.
@DudeHuLubeDaRubeCube:
I worked on these puzzles for quite some time. I am just publishing them as a batch.
See the image to find out which piece is equivalent to which RexCube-piece:
F => central Face of the Rex Cube
E => Edge of the Rex Cube
X => X-face of the Rex Cube