Have a close look at the enlarged view of one of the pyrite cubes. In particular, notice the damaged edge and the following:

• There is at least one spot that appears to have conchoidal fracture
• There don't appear to be any surfaces within the damaged edge that are flat and parallel to any of the faces on the cube, and over all, the edge has been broken in an irregular way.
• Also note that pyrite does have one direction of cleavage, but it is very poor cleavage.

All of this means that the flat faces on the pyrite sample, arranged as cubes with three sides at 90 degrees to each other, are there because of how the pyrite crystals grew, not because of cleavage.