It's been several hours that I try to design a puzzle in solidworks, and after several failures, I decided to ask for some help.
At the same time I think that it is a challenge because I think that this type of cuts doesn't exist, and I'm begining to think that it is impossible.

So the mech is a mix of a 4 axis core and 2x2 cuts(6 axis). (I'll keep secret the puzzle)
The problem is that with the 2x2 moves, the 4 axis misalign and bandage those moves.
Sure, I liked to create it myself, so that it's my own creation, but I dont think I have the knowledge and the experience to do it.

Additional info:
As everybody know, a 4-axis puzzle has 8 turning cuts, but only 4 are attached to the core to allow turning.
Also, the 8 cuts are not all the same, ex: in a skewb, the corners are not all the same, some cuts are inward and other outward.
But for allowing the 2x2 moves, the pieces need to be all the same or it will bandage. So i used 8 same cuts,but it can no longer be attached to the core.
To fix that, I used an extra layer. For now, my 2x2 cuts are just plain cuts.

The mechanism must be small ,because it is in a tetrahedron (hint).

So the aim of this topic is to help me better understand complex shell mechanism and ultimately find a core that enable 2x2 and 4 axis (skewb like) moves.

I will post later some of my prototype to give you lead or for inspiration. Thank you.

I think it's not much use being this vague... There are not many puzzles you could be making. In any case, it's hard to help without knowing the exact puzzle.

The only way to do it would be to get rid of the idea of using a 4-axis core and treat it as a 8-axis puzzle. Have a look at the mechanism of the FTO.

Sounds like you're either trying to make tetrahedral skewb + 222, or master skewb + 222.
if the second, use a split 8 axis core, like Tom said.
If the first, you can technically bandage the above 8 armed core puzzle in to a deep cut version, but try building instead the six axis core on top of the four axis core.

If knowing what is the puzzle will help you to help me (weird phrase ), here it is:

a rex tetrahedron + 2x2, that will allow jumbling + massive shapeshifting

Well, the most logical way to make it would be to build it up from a Dino Cube but this approach has proven problematic with Jason/Adam's Skewb 2x2x2. You could also treat it as a corner turning rhombic dodecahedron and do a "normal" shells buildup.
I'm not sure how it would jumble though.

First, what I mean by jumbling is that on a regular rex cube these pieces cannot be exchanged:

I dont have a rex cube, so it may be false.

Secondly, simply a rex tetrahedron was my first idea, but as I discovered that it doesn't jumble, it wont shapeshift either(in tetrahedron shape)

Thirdly, I found a solution and it wasn't hard. In fact, pretty easy. The problem was that my cuts weren't very good and because of that, the hidden corners that are usually attached to the core were deleted. So I just changed the cuts orientation (inward-outward) and those pieces reappeared.
After that, I figured that one turn doesn't move the other corner, so I just need to build a 8 arm spider over a 2x2.

Finally, this topic is just a waste of time and I have revealed my puzzle idea

Well, I'm glad you got it to work after realizing that an 8 axis-core would work better. Though I'm not sure if those corners are indeed stationary.

In any case, that is not jumbling. It's just changing the orbits (or something!). Though it would still change shape if you got the mechanism right, I think.

I could be way wrong here. But don’t pieces need jumbling for pieces to leave their orbits?

Nope. The hybrid of another puzzle can allow orbits to be changed.

I don't know if your talking about just a rex tetrahedron or with the 2x2 cuts, but for the first case, no it won't change shape:


But for the second case, YES! it shapeshift. First, 2x2 cuts on tetrahedron = pyramorphinx (or "phix"). And secondly, with the change of orbit, the center triangle and the corner-edge can switch.

Note: the image is not the rex+2x2

We seem to have very similar ideas ...