C₇₀ as a Molecule: Topology, Geometry, and Astrophysical Signatures

C₇₀ (D₅h) is notable among spherical fullerenes for an interesting correlation in which D₅h symmetry isassociated with a bond-length gradient that is simultaneously observed in ¹³C NMR chemical shifts, IR-activemodes, and astrophysical spectra of planetary nebulae. The combinatorial invariantΛ₁²/2 = V⁴/32(V + 4)² = 137.018 follows solely from Euler's formula and appears to be unique to C₇₀ in theseries C₂₀–C₁₂₀. The bond-length gradient δl = 0.069 Å (Hedberg et al. 1997), combined with Badger's rule,predicts IR-mode splitting δν ≈43 cm ¹, consistent with the experimentally observed value of 44 ⁻ cm ¹ ⁻(Δ0.1 cm ¹). Prediction P1: JWST MIRI MRS should resolve the 17.4 ⁻ μm band into two peaks (δλ ≈ 0.15 μm)in Tc 1 and related nebulae — JWST GO Cycle 3 (Cami et al.) targets this measurement. This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors