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Applicability of the Lie group F4 to the atomic f shell

The quark model of the atomic f shell, in which the angular properties of the states of the electrons are represented by the quark configuration (s+f)4, is generalized by assigning spins I=2 and 1 to the s and f quarks. This provides 5s+3f as a basis for the 26-dimensional irreducible representation (IR) of F4 and corresponds to the inclusions F4 contains/implies SOI(3)*G2 contains/implies SOI(3)*SOL(3). The shift operators I+or- make it possible to connect different IR's of SO(8) such as the three IR's of dimension 8, any one of which can be taken to span the 8 states of s+f in virtue of the automorphisms of that group. The additional symmetries associated with null triality are thereby subsumed. Application of the Wigner-Eckart theorem to SOI(3) provides a new perspective on relations between matrix elements of atomic operators within the f shell.