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True trimorphic cocrystals, i.e. multi-component molecular crystals of identical composition that exhibit three polymorphic structures, are exceedingly rare and so far no halogen-bonded cocrystal system was reported to exhibit trimorphism. Here, we describe a unique example of a trimorphic cocrystal exhibiting both hydrogen and halogen bonds in which the difference between polymorphs arises from their orthogonality evident by apparently independent variation of hydrogen- and halogen-bonded motifs.