A combined theoretical and experimental approach is used to recognize the sterochemical patterns which emerge when X(2) (X=H, halogen, etc.) is added to C-60 to form C(60)X(n), and the patterns formed by rings which incorporate carbon atoms of the fullerene, C-60(ring)(n). Addition to form C(60)X(2) occurs either at an edge linking two hexagonal faces on C-60, or across the para-positions of one of the hexagonal faces. Further addition occurs to produce potentially a very great number of isomers, but in some cases at least the pattern emerging is relatively simple. An important feature is the tendency of hexagonal faces with low degrees of addition, for example C6H2 or C6Br, to add further groups to form C6H4 or C6Br2 for example. This feature results in the production of chains, formed by the edge sharing of these hexagonal faces, which progressively increase in length as the extent of addition increases. Particularly stable structures are formed if these chains eliminate the chain ends to form cyclic structures. Examples include the skew pentagonal pyramids in C(60)X(6), C(60)X(12) and C(60)X(18), the crowns in C(60)X(18) and C(60)X(36), and the rhombicuboctahedral pattern in C(60)X(24). The ring compounds C-60(ring)(1-6), formed by additions to hex-hex edges, have rings occupying octahedral sites about the C-60.