The simplest irreducible 3-dimensional finite reflective group is tetrahedral symmetry, [3,3], order 24, . The reflection generators, from a D 3 =A 3 construction, are matrices R 0, R 1, R 2. R 0 =R 1 =R 2 =(R 0 ×R 1) =(R 1 ×R 2) =(R 0 ×R 2) =Identity. [3,3] () is generated by 2 of 3 rotations: S 0,1, S 1,2, and S 0,2. A trionic subgroup, isomorphic to [2,4], order 8, is generated by S 0,2 and R 1. An order 4 rotoreflection is generated by V 0,1,2, the product of all 3 reflections.