In this article, we analyse the common substructure of the Carlsbad twin in terms of the (pseudo)-eigensymmetry of the crystallographic orbits. In the case of the monoclinic polymorphs, all the orbits in the highest subgroup compatible with the twin lattice possess a (pseudo)-eigensymmetry which contains a restoration operation corresponding to the twin operation, which implies a high degree of structural restoration. This structural restoration is realised for twin elements located at distance one half the length of the unit cell, which explains the high occurrence frequency of this twin and its occurrence as both contact and penetration twin, and as primary or synneusis twin. In the case of triclinic polymorphs, the common substructure is much less satisfactory and the Carlsbad twin is probably inherited from the monoclinic phases, accompanied by transformations twins, or by late-stage synneusis, where mechanical adherence on prominent faces plays a more fundamental role.

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