In addition to spherical object such as C60, it is also possible to construct structures with spheroidal and toroidal shape by beading. The most difficult part of the construction is that we have to figure out the correct connectivity between different beads. I will discuss this issue later.
Here are the simplest beaded toroids with 120 carbon atoms I made.
The first molecule has D5d symmetry.
Another C120 isomer is a chiral molecule.