Extended Average Level (EAL) Dirac-Fock calculations on atoms and ions agree with earlier work in that a rough shell-filling order for the elements 119-172 is 8s < 5g≤ 8p(1/2) < 6f < 7d < 9s < 9p(1/2) < 8p(3/2). The present Periodic Table develops further that of Fricke, Greiner and Waber [Theor. Chim. Acta 1971, 21, 235] by formally assigning the elements 121-164 to (nlj) slots on the basis of the electron configurations of their ions. Simple estimates are made for likely maximum oxidation states, i, of these elements M in their MX(i) compounds, such as i = 6 for UF(6). Particularly high i are predicted for the 6f elements.