Fused fullerenes and multiply connected carbon clusters: Proposed new forms of carbon

We explore forms of carbon obtained from fusing fullerenes and demonstrate that (i) they are energetically more favorable than toroidal forms, and (ii) for small sizes, doubly connected structures resembling gears provide local minima where the strain is reduced via the formation of fourfold coordination. Some of these structures can be treated as a ``superatom'' which, when used as a building block for the solid, yield a crystal with fourfold coordination for all atoms, but with two-thirds the density of diamond. The recent experimental results reported may already point to the existence of fused fullerene structures.