This

mechanical puzzle is another variation on

Rubik's cube.

In completed form it is a cube and each face has a distinct
colour, similarly to the Rubik cube. It has three layers.
The top and bottom layers are are both divided into pieces
by lines through the centre of the face.

A A
__________
| |
| |
A | | A
| |
A | | A
| |
| |
----------
A A

In the diagram the lines I'm talking about join each A to its opposite A
(via the centre of the square).

This creates 8 pieces: 4 edge pieces and 4 corner pieces.
The edge pieces make an angle of of pi/6 at the centre
and the corner pieces make an angle of pi/3.

The middle layer is cut into two pieces by
one of the cut lines
of the other two layers. When a cut line for all the layers
is aligned it is possible to twist either half of the cube
about the cut line by an angle of pi.

This takes pieces from the top layer to the bottom layer and
vice versa. Such a move will also change the shape of
the top and bottom layers; they will no longer be square.
In fact there are 10 different possible shapes that can occur here.

The basic moves you make are combinations of the pi twist
and rotations of the top and bottom layers.

The square 1 is different from the Rubik cube in that
it is possible to mix up corner and edge pieces. This makes it
particularly interesting (and a fiendish piece of engineering).

The easiest way to solve it seems to be first get a basic cube shape
(with the colours messed up) and then to make move sequences that
preserve the cube shape (or almost do).

The Rubik cube is quite easy to disassemble without destroying it.
I don't know if the same is true of square 1. If anyone has done it without
breaking it, /msg me.