There are 49 heptacubes that have a pentomino P on one face. To my knowledge, this is the only “complete” polycube set that has a volume of 7³.

In May/2008 I constructed a set of these, using glued LEGO. A picture of these is shown below. Red pieces have a normal P, yellow pieces have a reversed P, and the white piece has both P orientations.

To see a step-by-step packing of the 7x7x7, follow this link: P-Faced Heptacubes packed into 7x7x7. The solution contains a hidden message at step 16.

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