9.24: Twin lattice
A twin operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent. The (sub)lattice that is formed by the (quasi)restored nodes is the twin lattice . In case of non-zero twin obliquity the twin lattice suffers a slight deviation at the composition surface.
Let H* = ∩ i H i be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D( L T ) the point group of the twin lattice and D( L ind ) the point group of the individual lattice. D( L T ) either coincides with D(H*) (case of zero twin obliquity) or is a proper supergroup of it (case of non-zero twin obliquity): it can be higher, equal or lower than D( L ind ).
- When D( L T ) = D( L ind ) and the two lattices have the same orientation, twinning is by merohedry (twin index = 1). When at least some of the symmetry elements of D( L T ) are differently oriented from the corresponding ones of D( L ind ), twinning is by reticular polyholohedry (twin index > 1, twin obliquity = 0) or reticular pseudopolyholohedry (twin index > 1, twin obliquity > 0).
- When D( L T ) ≠ D( L ind ) twinning is by pseudomerohedry (twin index = 1, twin obliquity > 0),reticular merohedry (twin index > 1, twin obliquity = 0) or reticular pseudomerohedry (twin index > 1, twin obliquity > 0).