A Short Review of Crystallographic Point Group T: Orbits and Stabilizers for a Regular Tetrahedron

The clear definitions of symmetry operations (or elements) of the crystallographic point group T (tetrahedral group) were clearly pictured. For each element of the group, the permutation (P4) counterparts and the matrix representations were obtained. The orbits and stabilizers for vertices, edges, and faces of a regular tetrahedron under the action of T and, by this way, some subgroups of T were found.