2,4,6-triaryloxy-1,3,5-triazines (POT) form in general molecular diads, termed as Piedfort Units (PU), in their crystals and their clathrates. Their bulky phenyl substituents (R = Me, F, Cl, Br, I, CN) in ortho, meta or para position substantially hinder internal rotations. Instead, non-crystallographic rotations (ncr) or translations (nct) are the bridges between the semirigid homologues or analogues, occasionally polymorphs. They occur in the space groups R3c (161), R 3 (148), P 3c1 (165), P6 3 /m (176), P 31c (163), P2 1 /c (14), Ia (9), and P 1 (2). In each group, the molecules are close to be isometrical, while these groups are linked by non-crystallographic symmetries termed morphotropism. The observed non-crystallographic symmetries are virtual between the homologues and real between their dimorphs. Real ncr's were also found between 4-RPOTs and their clathrate forms. It is demonstrated how e.g. toluene induces real nrc's in its clathrate with 4-IPOT.