The factorization of ligand field parameters into angular and radial contributions is examined. The angular term breaks up into a product of geometric and chemical environment tensors each of which contributes to the magnitude of the distortion parameter. The purely geometric function may be expressed as axial projections which need not represent metal-ligand bond positions. This permits direct comparison of D ndand D nhgroup properties. This projection description involves no approximations and since the operators are Normalized Spherical Harmonic Hamiltonians the derived radial integrals are all scalars of the octahedron and comparable between groups in different subduction chains. The projection factorization aids the description of intermediate symmetries. The tetragonal antiprism, the trigonal prism and the trigonal bipyramid each are capable of intermediate symmetry derived from cubic figures. In each case the Hamiltonian contains only one independent parameter. Each of these special conditions can be used as the geometric origin in distortion space diagrams. The radial function r 4 is shown to be a function of n 8. Only a small increase in the principal number n of d Orbitals is needed to account for observed values of DQ and these are justified using a United Atom model of transition metal complexes. The ratio of radial functions A 1 in distortion parameters then represents slight variations in n induced by different ligands.