Parametric Pyramid Puzzle

This puzzle has only 5 pieces of different shape, but identical volume. The resulting tetrahedron is nearly completely filled, with one secret void left.
Each piece again is built just from regular tetrahedrons and octahedrons. I designed this puzzle decades ago, carving some prototypes from wood. This implementation in OpenSCAD allows to adjust a few parameters:
1. Overall size: Limited by the printing area of your 3D printer. A 20 cm x 20 cm printing bed can just accomodate a 100 mm pyramide.
2. Sanding: In order to accomodate for various printers and materials, I introduced a "sanding" parameter which can be adjusted such, that the overfilling with material is JUST compensated.
3. Groove: Then, the depth of the groove between the triangle faces can be adjusted to taste (or no groove).
4. Mirror: Finally, the original arrangement of the pieces can be mirrored.

A simplified version of the puzzle - yet not simpler to solve - is now published being thing:4180442