A 'Perfect Cuboid' (also called a Perfect Euler Brick) is a (proposed) cuboid whose space diagonal also has integer length. That's to say a2 + b2 + c2 = g2 (where a, b, c are the sides and g is the diagonal).
There is currently no mathematical proof to determine whether they are possible physical structures or not. Computer modelling searches (running to trillions of examples) have so far failed to find one.
Further reading : Wikipedia