The rectangulated carbon structure can be formed by buckling the graphene layers of graphite and linking them together with four-membered cyclobutane-like rings. Baughman et al. proposed rectangulated carbon as a candidate for the structure of the transparent phase of carbon that forms upon room temperature compression of graphite. Here we present a full-potential linear augmented plane wave (FLAPW) investigation of the stability and equation of state of rectangulated carbon, The total energy and equation of state of graphite and diamond are also calculated for comparison with rectangulated carbon, The local spin-density approximation (LSDA) and the generalized gradient approximation (GGA) give similar results for diamond and rectangulated carbon, but different results for graphite. The pressure estimated for the transition from graphite to rectangulated carbon using the LSDA is slightly higher than is observed for single crystal graphite. The energy differences between diamond and rectangulated carbon are in accord with earlier calculations. The agreement at 25 GPa between the calculated diffraction pattern for rectangulated carbon and the observed diffraction pattern for transparent carbon is not as good as the agreement at 0.1 MPa.