The polytypic structures of vaterite, CaCO3, 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 CO3 groups. The two-sided layer group of symmetry of the OD layer is c2/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 P6122, P6522, C2/c, C2/c2/m21/m, and a more complicated sequence P312 or P322, 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 p32 and their stacking does not lead to polytypism and OD phenomena; these are generated on the Ca-based OD layers.

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