C₇₀, C₈₀, C₉₀ and carbon nanotubes by breaking of the icosahedral symmetry of C₆₀

The structure of particular hollow-cage fullerenes is described in exact coordinates, and their existence explained from a symmetry-breaking mechanism starting from the perfect icosahedral symmetry of C₆₀. The mechanism is extended to also describe the possible construction of larger nanostructures such as carbon nanotubes, as well as sets of stereoisomers of the C₆₀ molecule.