This puzzle looks a bit like a skewb and the dodecahedron faces seem to turn like a skewb. It's about the size of a standard cube, maybe a little smaller and is in fact built around a standard 3x3x3 mechanism.
As with the mastermorphix, it takes a while to get used to the fact that you are holding a cube. This is easier to do since the puzzle does not change shape. The clincher is not being able to use any skewb moves on the puzzle.
The 4-sided pyramid pieces are the face centres, the 3-sided pyramid pieces are the corners, the rectangles are middle edges. As with the mastermorphix, the face centres are sensitive to orientation. The middle edges are not sensitive to orientation and corners work as they do on a cube. When you get over the confusion, the only fly in the ointment is parity on the last layer.
All in all, this is an interesting variation on the cube and a cute little puzzle.