Also known as the Pocket Cube, Mini Cube or the Ice Cube.
Finally I had the patience to solve this cube.
It turns out that it's actually very simple and why it took me this long to analyse it I don't know.
First step is to complete the bottom layer with one colour and the four pieces in the right positions and rotations.
I won't describe the method to do this as it is quite trivial and you must have the skills to be able to that on your own to continue.
To solve the upper layer I have two simple rules that allow you to get the pieces in the correct positions and in the correct orientation.
The first rule allows rotation in one direction of three pieces .
The second rule allows the swapping of two neighbouring pieces.
The idea is to get the pieces in the correct positions and then rotating them to solve the cube.
You probably need to use the second rule to swap two pieces and then apply the first rule.
Looking at the top layer you can always find a particular orientation that applying the first rule you just have one piece in place with the correct colour showing in the upper layer.
After that you can apply the first rule several times to rotate the three remain pieces correctly.