0026: Utopian 2-Piece-Cube

Up to now, I already did nearly all kinds of puzzles: put-together, disentanglement, tanglement, interlocking, route-finding/maze, sliding and paper-puzzle/folding. The puzzle that I want to present now does not fit into one of those categories mentioned. It fits into the new category which is called "impossible objects". At first, the definition of a puzzle being an "impossible object" has to be given: "The puzzle is to explain how an object was made or why it behaves in a seemingly impossible way." [Mechanical Puzzle Classification of Jerry Slocum]

Starting with that definition I found an interesting and nice puzzle ...
It is a small cube of size 3cm x 3cm x 3cm. The cube consists of two rigid pieces. The following picture shows a perfectly made example with two contrasting woods:

The puzzler has to be given the following information:

the whole puzzle consists of exactly two rigid wooden pieces
the red wooden parts of the puzzle belong to the first piece and the yellow wooden parts of the puzzle belong to the second piece
the two pieces can be seperated from each other (!)
there are no parts within the pieces that have a "thickness of nearly 0 mm"

It has to be mentioned that the back of the puzzle (that cannot be seen in the picture) shows exactly the same structure as the front. So there is no trick.
The question is: How do the shapes of the two pieces look like (when they are seperated)? And how can the two pieces be seperated?

Try to figure it out ...

The following pictures show my first prototype of this puzzle. It is far away from being manufactured perfectly, but it worked. The "1"s and "2"s indicate, that these parts belong to piece number "1" and piece number "2". But how do the pieces look like such that they can be seperated from each other?