A review of recent structure determination of non-metal anions containing simple ligands, mostly halogenes, is given, where the total number of ligands exceeds 6. It will be shown that these anions exist in the form of regular polyhedra, the pentagonal bipyramid and the square antiprism. A non-bonding electron pair (or two) will influence such geometries in a complex way: the general principle that such pairs are stereochemically active needs to be carefully revised in compounds of large coordination numbers.