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An improved crystal structure model has been established for the β2 polymorph of the symmetric mono-unsaturated triacylglycerol 1,3-distearoyl-2-oleoylglycerol (SOS) and the equivalent β-V polymorph of Ivory Coast cocoa butter. In addition, the crystal structures of the β2 polymorphs are reported for the triacylglycerols 1,3-dipalmitoyl-2-oleoylglycerol (POP) and 1-palmitoyl-2-oleoyl-3-stearoylglycerol (POS), which are, together with SOS, the major components of cocoa butter, and that of 1-stearoyl-2-oleoyl-3-arachidoylglycerol (SOA). The existence of β2-POS and β2-SOA has not been previously reported in the literature. All structures have been solved from high-resolution laboratory or synchrotron powder diffraction data with the direct-space parallel-tempering program FOX and refined with the Rietveld module of GSAS. All compounds crystallize in similar monoclinic unit cells (Cc) with very long b axes (> 127 Å). The oleic chains are packed together and sandwiched between saturated chain layers, forming acyl-chain three-packs. An analysis of the β2 polymorphs and β1 polymorphs [van Mechelen et al. (2006). Acta Cryst. B62, 1121–1130] shows that they contain the same three-packs and differ only in the symmetry relation between the three-packs. The three-pack build-up provides an explanation of the mechanism of the phase transition that causes the formation of fat bloom on dark chocolate.