I can't find any videos of this thing turning, and I don't have one, but my guess is that it's basically a 4x4. You'd probably have an easier time using commutators than using a normal 4x4 method, though.
Look for 4x4x4 octahedron, which is basically the same puzzle as the one you have. I believe there is a thread about it on the twistypuzzles.com forum. Look for it in the "solving puzzles" section.
if i understand the sq2 case, put it on ful and bud and do 2,0 / (3,3) / (-1,0) / (2,-4) / (4,-2) / (0,-2) / (-4,2) / (1,-5) / (3,0) / (3,3) / (3,0)
for the pyraminx prystal, i think stefan has some videos of comms, and idk about the millstone but it like kind of like a skewb mechanism