MONKEY POD GAMES Soma Cube 3D - Large

Are the individual pieces the EXACT same shapes as the original Soma shapes? This is important, because the piece that you show in the photo IS NOT.

Is there a book of puzzles included with this? I especially loved Piet Hien's original book.

One of the reviews says that it comes with a cover/lid also that is not shown in the picture nor in the description. Does it come with a lid?

What kind of wood is it made of? The 2 pictures look very different.