  There are parallelepipeds with edge lengths, face diagonal lengths and body
diagonal lengths all positive integers. In particular, there is a
parallelepiped with edge lengths 271, 106, 103, minor face diagonal lengths
101, 266, 255, major face diagonal lengths 183, 312, 323, and body diagonal
lengths 374, 300, 278, 272. Focused brute force searches give dozens of
primitive perfect parallelepipeds. Examples include parallellepipeds with up to
two rectangular faces.
