Abstract :
In the physical context of symmetry-adapted bases for NMR spin (sub) systems and the spin statistics of ro-vibrational spectra, [A]24 (SU2 × 24↓ ) exo-cage cluster spin symmetry is derived, utilising both the corresponding isomorphic t-Octahedral cage rotational symmetry of certain specific isotopomeric fullerenes - e.g., [13C]24+/−, or [12C]nn [X]24 (SU(m)× 24↓ ) - and the specifics of Cayleyʹs theorem for [A]24 models, or for [13C..]60 symmetry [from Molec. Phys. 79 (1993) 934]. In consequence for n = 24 identical to for = , within a further rotational symmetry isomorphism implicit in the (6, 6, 4) and (8, 8, 3) regular t-Octahedra of the [4–6] and [3–8] (bis-cyclo) cages, the analytic (i.e. totally combinatorial) forms are determined for the spin invariance sets and their {[λ] → Γ} correlative mappings inherent in a fully determinate ( 24 ) natural embedding. The confluence between geometry and combinatorical algebra over a spin (site) invariance set, reported herein, is especially rare in non-icosahedral n-embedded symmetries.
