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The polytypic structures of vaterite, CaCO 3 , described in recent literature, have been reinterpreted in terms of the order-disorder (OD) theory, which allows us to explain and systematize all the observed and predicted polytypes of the mineral in a unified fashion. In terms of this theory, the structure consists of OD layers that comprise a layer of calcium coordination polyhedra and the attached halves of the standing CO 3  groups. The two-sided layer group of symmetry of the OD layer is  c 2/ m , whereas the interlayer symmetry operations are three twofold rotation axes at 120° to one another, as well as a mirror plane in the common layer boundaries and partial  c  glide planes perpendicular to the boundary. Depending on the orientation of the active twofold rotation axis with respect to the above-defined layer mesh, performed independently in each stacking step, maximally ordered simple stacking sequences  P 6 1 22,  P 6 5 22,  C 2/ c ,  C 2/ c 2/ m 2 1 / m , and a more complicated sequence  P 3 1 2 or  P 3 2 2, as well as several complicated or disordered sequences is obtained (before eventual relaxation to a subgroup of a particular space group). A perfect copy of the vaterite OD layer occurs in the structures of the bastnäsite-synchysite polysomatic series of fluorocarbonates. In these structures, the REE layers, configurationally analogous to the Ca-based OD layer, have layer symmetry  p 32 and their stacking does not lead to polytypism and OD phenomena; these are generated on the Ca-based OD layers.

Vaterite: interpretation in terms of OD theory and its next of kin