Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162). Polycubes may be conveniently represented and visualized in the Wolfram Language using ArrayMesh. There are 1390 distinct ways to pack the eight polycubes of order n = 4 into a 2×4×4 box.

Conway puzzle | cube dissection | diabolical cube | pentacube | polyform | Slothouber-Graatsma puzzle | soma cube

ArrayMesh