The Sodalite group have sodalite stacking producing cubo-octahedral cages that contain the anions and cations which balance the charge on the ordered aluminosilicate network. The dominant elements and radicals in the cages then define the members. There are considerable possible substitutions amongst the cage contents, often leading to solution series between the members, especially with Lazurite, Haüyne, and Nosean.
Ideally the unit cell of Sodalite has Na4Cl in each of the two cages in the unit cell. The two sodalite cages in the ideal Nosean unit cell contain Na4SO4 and Na4H2O. Ideally the two cages in the Haüyne unit cell both contain Na3CaSO4. The two cages in Lazurite contain (Na,Ca)4(SO4,S3,S2). Only recently has it been found that sulfate dominates S in Lazurite. This situation of reminiscent of Hackmanite which has minor sulfide in the sodalite cage and consequently is a variety of sodalite. So Lazurite is really a sulfide-rich variety of Haüyne and should not be a species.
Vladirivanovite was first recognized as a triclinic and later an orthorhombic Lazurite with a modulated structure. The modulations arise from a rotation of the sulfate tetrahedra in the sodalite cages. In Tsaregorodtsevite the ordering in the Al and Si tetrahedra is lost as there are 5 Si atoms for each Al. Although Tsaregorodtsevite is orthorhombic, the frame work still has two sodalite cages in the unit cell and remarkably they each contain the organic N(CH3)4.
The Helvine Group may be considered a subgroup of the Sodalite Group. The Helvine Group are beryllosilicates with Be playing the role of Al in the sodalite group. The sodalite group has recently been considered as part of the Cancrinite Group. Both are aluminosilicates that differ by the stacking of the aluminosilicate honeycombs.