Polychromatic symmetry

If these three cases are present with equal frequency in an orderly array, then the magnetic space group of such a crystal should be three-coloured.

[5] Taking a single motif in the pattern p3[3]1 it has a symmetry operation 3', consisting of a rotation by 120° and a cyclical permutation of the three colours white, green and red as shown in the animation.

This pattern p3[3]1 has the same colour symmetry as M. C. Escher's Hexagonal tessellation with animals: study of regular division of the plane with reptiles (1939).

Escher reused the design in his 1943 lithograph Reptiles and it was also used as the cover art of Mott the Hoople’s debut album.

Senechal showed that the permutations are determined by the subgroups of the geometric symmetry group G of the uncoloured pattern.