After seeing the Cross Square-1 again, it occurred to me - could you do something similar with an FTO?

Maybe not with Square-1 halves on each face, but you could at least have 6 wedges or something.

Well I never designed anything (I don't got the money! lol) but I think that this is possible since
It's an FTO, 6 axis, so you can just put them at the ends of 6 faces
the cuts are through the middle, so a 2x2x2 cross type of thing like the sq-1 cross cube can be made
and lastly because of this http://www.jaapsch.net/puzzles/alex.htm that is close to what you're thinking, right?
Just noticed, that's pretty bandaged, if you want to do 2x2x2 turns you'll have to keep adjusting the hexagons.
Also check out SmaZ time machine.

I do believe it would be possible. You would probably have to change the angles of the cuts. (Maybe) But after that you could attach the inner rails to the FTO faces and assemble it and make it look nice. Doesn’t seem like TOO much work.

Hold up:

Take a 3x3, and put an FTO face on each face of the 3x3. An FTO has 3 axes of rotation. When you turn the layer, it wouldn't turn because the angle of a face rotation is different than that of a 3x3.

I think you are confused. This is an idea about putting Square 1 faces on an FTO. Not FTO faces on a 3x3x3

since the FTO turning planes intersect at the center of each face at an angle then you couldn't add a block to the outside of the face because there would be a floating piece in the middle (It's hard for me to explain so if you would like I can give a picture.) Perhaps you could add a ring to each face so the floating center piece would not exist. Also the square-1 pieces turn on little rings and the more you cut the rings up the turning becomes worse.

I see. My apologies.

No need to apologize just trying to help.

I’m sorry cubedude but I don’t get the floating pieces thing, Could you make a picture?

If you cut it shallower, like a Dino Octahedron (by Katsuhiko, I believe) and then extend, you will get something like an octahedral Trignis. However it would be extremely difficult to make them turn by multiples of sixty degrees, because adjacent cuts of the FTO do not intersect the main plane at right angles.

If the puzzle was printed the floating pieces could be held in just fine. If Solidworks didn't hate me I could make a mockup of this to show what it could look like.

Yes you probably could get the piece to stay in fine and I think it would be cool but if you wanted it to be like a square-1 then there would be no center piece. here is a picture that I hope explains what I mean. The floating center piece is blue. The second picture show an alternate option which eliminates the center piece.

Wouldn't it also be possible to use a shallower FTO as a base so that the cuts meet up at the center of the extended faces?

No offense but Yuck!!!

I can fully understand what you are going for but that ring just looks wrong. Maybe those six pieces could be a different shape to make it look better. A triangle with a triangle cutout maybe?

Will's idea would also work but the visible edges of the octahedron would look different.

Could you show the circle so that it covered everything except where the center would be?

more pictures! the 1st is will's idea and the 2nd is puzzle master's with shallower cuts. If it had normal depth cuts the triangle would have small pieces.

I actually designed an Octacano two months ago (like a vulcano/trignis except from an octahedron)

I might print it at some point too

(Not 6 pieces on each face, but 9 (all of them are crossed))