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It is possible to pack 6 of these pieces into the box in a way where it appears completely filled, with no room for any more pieces (or even one more sphere). This is an interesting way to present this puzzle to someone, can they add not one but two more pieces and close the box?
A box packing puzzle invented by Leonard Gordon more than 25 years ago. Originally devised from pieces made from joined spheres, here I use truncated rhombic dodecahedra or edge beveled cubes. The eight pieces are identical and sized so that they fit in a golf ball case.
Four of the pieces can also be interlocked to form a truncated tetradedron. This is a second puzzle, called "Blossom".
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