Confused Pillow Cube

Made by SOCUBE, Kuala Lumpur, Malaysia, 2009.
(plastic, 2.2 inches)

Like the Pillow Cube, this is the same puzzle as a Rubik's 3x3x3 Cube. However, as the name indicates, it is confusing because when orientated as shown in the photo above, the top and bottom layers do not rotate (e.g., referring to the front left corner, the two white triangles and the red triangle are part of a single piece). To see the correspondence with Rubik's 3x3x3, turn the puzzle on end so the horizontal planes correspond directly to those of a Rubik's 3x3x3 and each pair of vertical parallel diagonal planes correspond to the pairs of vertical planes of Rubik's 3x3x3; that is, this puzzle is like the Rubik 3x3x3 Fisher Cube with shaped sides. Here are photos of the other sides and how the puzzle moves: