Crystals of a new high-symmetry structural modification of Cs2HIn(IO3)6 which crystallizes in sp. gr. R \(\bar {3}\) with the unit cell parameters a = 11.8999(4) Å, c = 11.6513(5) Å, was obtained under hydrothermal conditions. The crystal-chemical comparison with the previously characterized triclinic modification of this compound was carried out. Both structures are composed of isolated [In(IO3)6]3– blocks. The new modification belongs to the family of trigonal iodates isostructural with the compound K2Ge(IO3)6. The local symmetry of individual [M(IO3)6] blocks (M = Ge, Ti, Sn, Ga, In, and some other metals) was analyzed. The structural systematics of iodate families was proposed based on the comparative crystal-chemical analysis. The influence of the cation composition and the synthesis conditions on the symmetry and topology of the crystal structures and the effect of the local symmetry of individual blocks on the physical properties of the compounds are discussed.