Yep, the 4 corners cube, and the clover tetrahedron (Lanlan's Star Pyraminx is technically a redesign of the clover tetrahedron) are indeed shape variants of each other.
The second one (four corners cube I think?) reminds me of the insanity cube. That problem with one corner flipped weirdly is something I remember struggling with a lot for the insanity cube. It's probably not exactly the same, but the idea is similar.
Dude I sincerely request you to make shorter videos. I understand that you want to give an in depth review, but it usually fails to grasp attention for the entire video. Again, no offence, just a fan suggestion. Thank you!
I think your last twisted pieces in the second puzzle is a parity. Maybe one of the leaf(ish) looking pieces is twisted as well as the obvious pieces. I dont know the best way to explain that. Only reason I say that is because the leaf(ish) pieces are in the same orbit as the twisted corner and the piece its paired with.
The 4 cornered puzzle, what is happening when you have just one group flipped is that one of the center pieces are flipped, to solve this just do the flipping alg but instead of doing it with another set of flipped grouped pieces do it with a center
Maybe my ears are just bad but it sounded like there was a bit more echo than normal, or it may just be a placebo of you recording in a new environment ;)
