Chocolate Box Puzzle

Pack the six "chocolates" into a cylindrical box and close the lid. Is it possible? The "obvious packing" (shown in the photos) is to place two pieces together in a layer and then repeat this three layers high. But this packing sticks above the top of the box, and the lid can't go all the way down.

Can you find the real solution, where all the pieces are packed below the rim of the box? In the real solution, the lid goes all the way down and it does not touch any pieces.

I made this puzzle fairly large. The pieces are 2 cm tall and the diameter of the box is almost 9 cm (3.5 inches).

The pieces are made from truncated rhombic dodecahedra, also called edge-beveled cubes. It is not a true truncation because only the degree 4 vertices are truncated.

To see a wood version of this puzzle look here. Contact me if you need the solution.