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Tetrahedron packing puzzle

Posted 11 years ago
There are several clear plastic boxes with a lid for 27 cubic dice.

I've had this idea for a similar box with tetrahedral dice, tightly packed.  For the puzzle, you take the lid off and dump them out, set the lid down, and challenge the person to pull the dice back in with the lid on.  This particular packing took mankind almost 3000 years to find, so it's challenging.

The tetrahedra would be in the Densest Tetrahedral Packing configuration. The clever part is in the lid, which has a starting surface for this configuration. To solve, the tetrahedra would be built on the interior of the lid, and then the box would be slid down over the tetrahedra and onto the lid.

To make this, someone would need to be willing to do 3-D printing of the lid after doing a careful study of available tetrahedral dice and plastic boxes.  Whould anyone like to try making this puzzle?
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