The structures of C-119 and C-129, the two lowest odd-numbered fullerenes, are investigated by semiempirical quantum chemical calculations, In the process, the use of a recently proposed parametrization for a tight-binding Extended-Huckel model is validated to study the relative stability of fullerenes. Three general routes for the generation of the structures of odd-numbered fullerenes are described and used to generate systems that can be loosely characterized as having either a four-membered ring or a patch of adjacent pentagons, or a set of multiple connections between the cages of the pristine fullerenes. The structures of the six isomers of C-119 obtained in this manner are optimized and it is confirmed that the most stable isomer of C-119 has C-2 symmetry and forms three bonds between the C-59 and the C-60 moieties. By analogy with C-119, 56 structures of C-129 an generated and their geometries are optimized, As in the case of C-119, it is found that the most stable isomer of C-129 can be formed both from the reaction of C-59 with C-70 and from the reaction of C-60 with C-69. On the basis of the calculation, five propensity rules for the stability of odd-numbered carbon clusters are proposed and a source of exception is discussed.