Derivation of the Shape of an Atomic Orbital from the Angular Nodal Planes and the Symmetries of Their Distribution

The shape of an atomic orbital not only depends on the azimuthal quantum number l, but also associates with the magnetic quantum number m. We discussed about how to derive the shape of an atomic orbital from the numbers and shapes of the angular nodal planes, and the symmetries of distribution of all angular nodal planes when l and |m| are known. According to the |m|, the compatibility of the symmetry of an atomic orbitals have also been also discussed.