release soon

Uh? It seems like a Pyramid based thing. It has the outer appearence of a truncated octahedron but not all the hexagonal faces are the same. Seems like there are two types. So It would be a Pyramid truncated twice.
?

Edit: Hm it has the cutpattern of a Master Skewb Octahedron that has been truncated on four sides and shallower cutplanes on the other four. I can't figure out what that is.

It appears to be a shape variant of Timur's F-Skewb.

I think I got it:



This is essentially a Master Tetrahedron (Master Skewb in Tetra shape).

The black lines show the cuts. The green lines are Truncations. After that the blue lines indicate the second truncation. That of the octahedron's corners. The shallower cuts are done in a way that the square faces formed by that second truncation split in the middle.
Building up on those surfaces would result in new parts. To be exact, one additional part between the intersecting cut planes on each square face. Those parts are the truncated octahedrons tips.

I hope I am right with all this.

EDIT: NO, this is wrong. Something is wrong with the blue lines. A truncation there wouldn result in square faces that are split in the middle. The cutplanes would go through the resulting edges of those faces.
DARN!

Sorry for being so jumpy.

What do you think about this now. This time I have it! I SWEAR!



The additional face cuts weren't shallow enough in my last one that's all.

This reminds me in the Gem IV, which is also based on a more complex puzzle, which was the FTO gelatinbrain 4.1.7 except the outer floating pieces removed by truncation.

As alaskoje found out by himself it can't be a "simple" Master Skewb variant because all hexagon would look identical in that case.
The cornerturning hexahedrons and puzzles with the same axis system have the special property to allow offset cuts => pairs of parallel cuts with different distance from the core.
The F-Skewb is one example of such a puzzle. The Pyraminx has offset cuts too.

Very exciting news.
Thank you juanan.

Yes and I just checked this statement and it is right. The F-skewb wasn't on my mind and for some reason I didn't even varify this after Luke had pointed it out. I never saw the relation between F-Skewb and this Pyramid puzzle either though.

I thought the Gem series had run it's course, so I'd be very happy to see new members! Am I correct that what makes this puzzle part of the "Gem" series is that it is a face-turning truncated octahedron?

I guess it's more about that weird shape of what you say. It has 8 hexagonal and 6 square faces. Thus it is a Gem. Actually I never liked that shape at all.
A F-Skewb would be much more awesome.

But that's just me.