Exclusively combinatorial invariance aspects of a non- [formula omitted] model (reg.-t) polyhedral 13C-fullerene: Cayleyan [A] 24 (SU(2 ⩽ m) × [formula omitted]24↓ [formula omitted]) NMR (R-V) spin symmetries and their correlative mappings

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 × L 24↓ O ) 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)× L 24↓ O ) - and the specifics of Cayley's theorem for [A] 24 models, or for [ 13C..] 60 symmetry [from Molec. Phys. 79 (1993) 934]. In consequence for n = 24 identical to | G | for G = O , 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 ( L 24 ⊃ O ) natural embedding. The confluence between geometry and combinatorical algebra over a spin (site) invariance set, reported herein, is especially rare in non-icosahedral L n -embedded symmetries.