The atomic models of [C-28 + C-4] fullerites based on C-28 fullerenes bound by acetylide C-2 bridges are offered. Their structural, elastic and electronic properties are predicted by means of the DFTB method and are discussed in comparison with topologically identical C-28 allotropes. The calculations show that, due to unique structure of [C-28 + C-4] crystals, they would be the lightest among all known fullerites, while their bulk moduli will be essentially higher, than those for more dense C-28 fullerites. We propose a possible route for the chemical synthesis of these structures composed of sp-, sp(2)- and sp(3)-hybridized atoms, which could be more successful, than previous experimental tests on adsorption of C-28 from gas-phase. (C) 2009 Elsevier B. V. All rights reserved.