Johnson identified two specific trionic subgroups of [3,3], first an index 3 subgroup [3,3] ≅ [2,4], with [3,3] ( = = ) generators {0,1,2}. It can also be written as [(3,3,2)] () as a reminder of its generators {02,1}. This symmetry reduction is the relationship between the regular tetrahedron and the tetragonal disphenoid, represent a stretching of a tetrahedron perpendicular to two opposite edges.