Solving the Axis Cube

This was a really fun puzzle, but I didn't understand which pieces would correlate to the proper position on a 3x3 cube. Once I made the bijection and figure out how to turn the puzzle properly it was really great stuff.
I really want to get one of Meffert's Ghost Cubes after this, but I hope you all enjoy the video. There is also a possibility you will not need to watch the entire thing, try it out on you own unless you just need a couple hints!

[@dummyload7803]

you are explaining it good but i dont know how to replace pieces or make them go where they are supposed to go so this will be unsolveable for me i guess. I only learned the "spiegel solution" from 197x

[@junkcuber5611]

What I would do is make a correlation from your 3x3 to this puzzle. Every piece of your 3x3 should match up with exactly 1 piece on this puzzle. Once you do that, set the cases up on your 3x3 and just solve the axis cube the same way.

[@dummyload7803]

@@junkcuber5611 the problem might be my brain. I can look at it as long as i want i do not get it (or see it)

[@junkcuber5611]

@@dummyload7803 have you done other 3x3 shape mods first?

[@dummyload7803]

@@junkcuber5611 no, no shape mods. I have others (Skewb) that i solved by accident :)

[@junkcuber5611]

@@dummyload7803 start with the mirror cube