Well, I finally took the plunge. I scrambled the Anisotropic Cube. One feature that I have observed about this cube, is that the eight corners always have fixed orientation with respect to the freely-turning layer, as do the Anisotropic pieces always align themselves onto the same plane. The Anisotopic Cube can probably be solved as a subset of the Rubik's Cube, were it not for those pesky little gears which seem to defy the natural logic of twisty puzzles. After a fair amount of manipulation, I came to the shocking conclusion that it is possible to only twist one gear while the remaining seven stay in perfect alignment with their corresponding 3x3x3 edges. Have a look...

There is no monkey business going on here: Despite not photographing the backside of this cube, I can assure you that none of the other gears have been twisted with respect to their edges, nor are any of edges in a "flipped" state. All of the red or black either faces up or down. Naturally, I thought this to be a contradiction, but upon closer inspection, I learned why: Every time you do an "LR" or "FB" move, each of the four gears along the center slice parallel to the receive a twist of -5/6. This is equivalent to a +1/6 (clockwise) turn for each of the four gears compared to their mated edge, hence every quarter turn of the opposite faces yields a +4 overall gear parity. But unlike it's Gear Cube sibling, on the Anisotropic Cube, the edges are not strictly confined to groups of four and are allowed to be freely scrambled. Because the least common denominator of 4 and 6 is 2, it is only necessary that the total twist metric of all gears merely be even. And since "even" can include a twist of +2/6 or -2/6 (+ or - 1/3), it is fully possible to twist only one gear out of alignment