I have two lesser known 3D puzzles similar to Rubik's cubes, which are
surprisingly more difficult than the cube. I don't know who invented
them, but I call them Rubik's Sphere and Rubik's Cuboid (see below).
To solve them it is necessary to find move sequences (I call them tricks) which interchange
only a few cubis.
Once you have these tricks, the ball/cuboid can easily be solved by suitably selecting and executing them.
The tricks are more difficult (to find) due to the reduced symmetry (as compared to the
cube and dodekahedron). There are directions
in which a 90° rotation is impossible. This prevents an adaption of some of the tricks from the cube.
Rubik's sphere consists of eight 45° sectors which can be rotated against
each other by 180° turns. It is also cut into 4 slices rotateable against
each other by 45°. Unfortunately, the mechanics of this model are very poor.
Rubic's cuboid consists of 2×3×3 cubis. Instead of the usual colors,
the cubis are numbered domino-like, but this is irrelevant for the
strategies. Again, only one direction allows 90° turns, in the other two
only 180° rotations are possible. The mechanics are extremely good.