Elastic, electronic and vibrational properties of seven models of nanoporous carbon are reported. The studied structures are periodic graphitic arrangements with heptagonal and octagonal rings of carbon, known as Schwarzites. The calculations were performed within a non-orthogonal tight binding framework which has been shown to be reliable for diamond, graphene layers, fullerenes and carbon nanotubes. In contrast with previous studies, each structure was properly relaxed, so that differences between each model must be assigned to intrinsic properties rather than to differences in their construction. Thermodynamic properties were calculated from the vibrational density of states.