A novel quasi-two-dimensional phase of carbon and the formation of a metastable hexagonal phase of single-walled carbon nanotubes (SWCNTs) have been investigated using density functional theory (DFT) by subjecting the SWCNT bundles to hydrostatic pressure. The chirality of the nanotubes determines the breaking of symmetry of the nanotubes under compression. Interestingly SWCNTs are found to undergo a mixture of sp(2) and sp(3) hybridization and are found to form novel interacting quasi-two-dimensional sheets of interlinked SWCNTs under hydrostatic pressure. Symmetry breaking, leading to the formation of highly directional bonds at stressed edges, is found to play an important role in the interlinking of the nanotubes. (3n + 3, 3n + 3) SWCNTs are found to acquire a hexagonal cross-section when subjected to hydrostatic pressures. The opening of a pseudogap is observed for small as well as large diameter armchair SWCNTs in nanotube bundles. Equilibrium separations calculated using the Leonard-Jones potentials indicate excellent agreement with the predictions of density functional calculations and experimental observations.