The magic Domino (available, at least, at Games People Play here
in Cambridge) is a delightful little puzzle. I would guess that it
is the easiest of the `Rubik-type' puzzles to date -- I think it is
even easier than the 2x2x2. I solve it with two basic moves:
one fixes the corner (but screws up the edges), and then the other
fixes up the edges.
An interesting sidelight on the domino is the ability to interchange
ONE pair of edges. The trick here (for reasons that I don't
understand yet) is that the supergroup rotation seems to invert the
parity of the edges. That is: if you have the whole domino solved
and then re-solve the thing with both faces rotated by a quarter turn
around the center (5) cube. You'll discover that you can't do this hardly
at all on just one face, since you wont be able to get the corners fixed.
But if you rotate both the white and black faces, then the corner parity
is OK, BUT.... the edge parity has been flipped and so you have done a
single interchange of two edges.