Structures and energies are calculated at the DFTB level for C-36-based fullerenes, hydrides, oligomers and solids. The two fullerenes with minimal pentagon adjacencies are isoenergetic. The isomer implicated in recent experiments has C-6 upsilon broken symmetry, a small HOMO-LUMO gap and can gain or lose up to six electrons. C-36 forms stronger inter-cage bonds than larger fullerenes. A favoured sigma-bonding pattern rationalises a dimer with ten times the stabilisation of (C-60)(2), a linear polymer, a 'superbenzene' oligomer, a 'supergraphite' layer and a hexagonal close-packed solid with a monomer stabilisation of 522 kJ mol(-1) and a d-spacing (6.82 Angstrom) compatible with the experiments. (C) 1999 Elsevier Science B.V. All rights reserved.