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
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.