Experiments are described in which polyimide was irradiated with 4 × 10 14 lithium ions/cm 2 (at MeV energies), and pyrolityic graphite with 10 12 dysprosium ions/cm 2 (at GeV energies). Chromotographic analysis of the irradiated samples revealed small but definite quantities of fullerene in every case, whilst none was detected in either the corresponding unirradiated material or the virgin solvent. The C 60 molecule (fullerene) has been previously macroscopically synthesized in flames, sparks, arcs, ablating laser beams, and under high dose-rate electron irradiation. A common feature is the high transient energy density, followed by a rapid “quench”. The new method described here is essentially microscopic, based on latent particle-track formation in condensed matter. A simple theoretical model for efficient fullerene genesis consists of a short (∼ 2 nm long) core of highly ionized carbon only ∼ 0.6 nm in diameter, wrapped about the energetic projectile ion. The lifetime of this is short (∼ 10 −15 s) relative to that of the energy deposition process (∼ 10 −12 s) over the long (∼ 200 μm) particle trajectory, so that primary excited electrons have very quickly lost their energy and remanent energy is vested in excited atoms . This core is the dense primaeval “gas” which most probably gives rise, in the absence of inhomogeneities and impurities, to homogeneous “nucleation and growth” of fullerene molecules (from C ∗ , C ∗ 2 etc). Fullerene formation most likely begins first at the outer track wall, and proceeds inwardly as part of the “quench”. This model for fullerene genesis is equally appropriate for earlier methods of experimental production. In each case a high energy density is required for a high volume density of excited carbon, and there is probably a critical lower threshold energy. The ability to transform graphite, and probably both diamond and amorphous carbon, to the new allotrope of carbon, also means that we are dealing with a phase transition of the first order — a “reconstructive transformation”.