A theoretical approach is used to recognise the stereochemical patterns which emerge when X-2 (X = H, halogen, etc.) is added to C-60 to form C60Xn. Addition to form C60Xn occurs either at a hex-hex edge, or across the para-positions of one of the hexagonal faces. Both these structural elements may occur in subsequent additions. An important feature is the nonplanarity of the hexagonal C6 rings resulting from some tetrahedrally coordinated carbon atoms, and the way this nonplanarity influences the conformations of surrounding rings. Further addition leads to the formation of chains of edge-shared hexagonal faces. Particularly stable structures are formed if these chains eliminate the chain ends to form cyclic structures. Examples include the skew pentagonal pyramids in C60X6, C60X12 and C60X18, and the crowns in C60X18 and C60X36. At higher levels of addition, in order to decrease X-X repulsions, it becomes necessary to spread the X atoms as evenly as possible over the surface, and/or to place some X atoms in endo-positions, and/or to disrupt the C-60 cluster. (C) 1997 Elsevier Science Ltd.