Full geometry optimization has been performed within the semiempirical QCFF/PI model for the 1812 fullerene structural isomers of C-60 formed by 12 pentagons and 20 hexagons. All are local minima on the potential energy hypersurface. Correlations of total enery with many structural motifs yield highly scattered diagrams, but some exhibit linear trends. Penalty and merit functions can be assigned to certain motifs : inclusion of a fused pentagon pair entails an average penalty of 111 kJ mol(-1); a generic hexagon triple costs 23 kJ mol(-1); a triple (open or fused) comprising a pentagon between two hexagonal neighbors gives a stabilization of 19 kJ mol(-1). These results can be understood in terms of the curved nature of fullerene molecules : pentagons should be isolated to avoid sharp local curvature, hexagon triples are costly because they enforce local planarity and hence imply high curvature in another part of the fullerene surface, but hexagon-pentagon-hexagon triples allow the surface to distribute steric strain by warping. The best linear fit is found for H, the second moment of the hexagon-neighbor-index signature, which fits the total energies with a standard deviation of only 53 kJ mol(-1) and must be minimized for stability; this index too can be interpreted in terms of curvature.