Ranges of the [CH]/[CH₂] ratios for all of the considered models: tetrahedra and octahedra including their truncated forms, solid red and blue lines, respectively.The dangling and rising thinner lines show the effects of increasing truncation. The dashed lines show the [CH/[CH₂] ratios for the regular polyhedra: T (red), tT (orange), O (blue), tO (purple), cO (cobalt), and tC (green). For cubic particles (C) this ratio is zero. The black squares show the ratios for ‘spherical’ nano-diamonds and the orange dashed line shows an analytical approximation to these data (see text for details). The grey shaded gives an indication of the observed and experimental values (0.5–3) and the lighter grey vertical band indicates the typical radii of the most abundant pre-solar nano-diamonds (1.3–1.5 nm).