Transposable domain pairs and domain distinction

We divide pairs of domain states into three classes: Completely, partially and non-transposable domain pairs. We show that two groups can be associated with a domain pair: The twinning group and the symmetry group of the pair. The twinning group determines which secondary order parameters are the same and which are different in two domain states of a domain pair. The symmetry group of a transposable domain pair allows one to express the order parameters and irreducible constituents of material property tensors in such a way that their components in two domain states are either the same or differ only in the sign. The analysis of domain distinction is illustrated on a simple example.