Abstract 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,I, can be extended to unity and negative odd integers. Polarity reversal domains are characterised byI=–1 andnth order inversion twins byI=–(3)n. The partial symmetry operations producing coincidence and anticoincidence lattices are discussed.