The evidence for the occurrence of polarity reversal domains and inversion twins in compounds with the wurtzite and sphalerite structures is reviewed. Anti-coincidence lattices are defined for orientation relationships such that a fraction of sites of the two lattices coincide, but wrongly, to produce anti-coincidence sites. Proceeding from Friedel's theorem, the range of Friedel indices, 1, can be extended to unity and negative odd integers. Polarity reversal domains are characterised by / = --1 and n th order inversion twins by / = --(3) n. The partial symmetry operations producing coincidence and anticoincidence lattices are discussed.