Combining density functional theory computation and the global minimum structural search, we have found new a-, b-, and d-phographene carbon allotropes. The a-phographene is almost degenerate in energy with the previously reported phagraphene, which is energetically favorable as compared to the band d-phographenes and the other known non-honeycomb two-dimensional carbon allotropes. Our careful studies of the a-and b-phographenes show good dynamic, thermal, and mechanical stabilities.The pristine a-and b-phographenes are metallic, which would be altered to wide-gap semiconductors by hydrogenation. Additionally, the a-phographene shows enhanced joint density of states at the energy of $1.6 eV, which may find applications in photoelectronics. The analyses on the growth of structural motifs and the effects of net charge suggest the possibilities for experimentally fabricating aphographene. Interestingly, the a-phographene has a Young's modulus and Poisson's ratio close to those of graphene, showing remarkable mechanical properties. It may also find applications in supporting Au or Pt clusters as high-performance complex catalyst nanostructures, calling for further investigations on both theory and experiment.