Derivation of possible framework structures formed from parallel four- and eight-membered rings

The number of possible combinations of parallel four-membered rings, of the same kind, forming an eight-membered ring is systematically derived by a different method from that of Smith & Rinaldi [Mineral. Mag. (1962). 33, 202-211]. 17 different configurations (including six enantiomorphic) in the UUDD ring (U and D represent upward- and downward-pointing tetrahedra respectively), four different ones (two enantiomorphic) in the UDUD ring, and sixteen different ones (seven enantiomorphie) in the UUDD ring are shown with their new pattern representations and symbol notations.