The , and cubes can be filled with a polycube "snake" that turns by right angles at every step. The solutions for these three cubes are given here.[more]
The display of the polycubes is optional; their positions are represented by black points connected by a polyline.
Such a snaking path can be found for all cuboids except for the following cases:
odd, odd, .
(Karl Scherer 1982; the proof is very easy.)[less]