Abstract
All the colored crystallographic and icosahedral point groups that obey the van der Waerden and Burckhardt definition are tabulated here, using a symbolism based on a suggestion of Shubnikov and Koptsik. Each asymmetric domain of the object has a single color - or scalar quality. The symbol of each colored point group G(H' | H) contains G, the geometrical point group of the object; its sub-group H' that is the point group of each of the object's monochromatic domains; and H, the invariant subgroup of G that is the intersection of all the conjugate subgroups H'. If H' and H are the same, the symbol G(H' | H) is changed to G(H). If H is chiral, so is the colored point group. If G is not chiral, but H is, the chirality is only chromatic. These phenomena are listed in the table. If more color permutations are possible than occur in the operations of a colored point group, different arrangements of the same colors on the same geometrical object are fundamentally different: these are called diamorphs of each other; their number is listed. 'Color', as used here, symbolizes any scalar property that can vary from one asymmetric domain to another.
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