Editing Polycube (section)

==Symmetries of polycubes==
As with polyominoes, polycubes may be classified according to how many symmetries they have.  Polycube symmetries (conjugacy classes of subgroups of the achiral [[octahedral group]]) were first enumerated by W. F. Lunnon in 1972.  Most polycubes are asymmetric, but many have more complex symmetry groups, all the way up to the full symmetry group of the cube with 48 elements.  There are 33 different symmetry types that a polycube can have (including asymmetry).<ref name=symmetry/>