Enumeration of polytypes MX and MX₂ through the use of the symmetry of the Zhdanov symbol

The number of possible close-packed polytypes MX and MX₂ for repeat P have been calculated through elementary combinatorics for each possible space group.

Zhdanov's rules work both ways

The mapping between the possible space-group symmetry of a periodic stacking of layers of close-packed balls and the possible two-dimensional two-color point-group symmetry of the cyclical representation of its Zhdanov symbol is shown to be a bijection.