A nice 3D puzzle similar to Rubik's cube
is Rubik's dodekahedron which has 12 regular pentagon sides, each consisting of
5 vertices, 5 edges and one middle.
To solve
the dodekahedron it is necessary to find move sequences (I called them tricks) which interchange
only a few cubis. This was the difficult part.
Once you have these tricks, the dodekahedron can easily be solved by suitably selecting and executing them.
The solution I found is similar to that of
the cube.

My Rubik's Dodekahedron

My Solution for Rubik's Dodekahedron

With these tricks it is easy to figure out how to combine them and to solve
the dodekahedron.