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We propose general principles to construct two-dimensional (2D) single-atom-thick carbon allotropes. They can be viewed as the generalization of patting Stone-Walse defects (SWDs) by manipulating bond rotation and of patting inverse SWDs by adding (or removing) carbon pairs on the pristine graphene, respectively. With these principles, numerous 2D allotropes of carbon can be systematically constructed. Using 20 constructed 2D allotropes as prototypical and bench-mark examples, besides nicely reproducing all well-known ones, such as pentaheptites, T-graphene, OPGs, etc, we still discover 13 new allotropes. Their structural, thermodynamic, dynamical, and electronic properties are calculated by means of first-principles calculations. All these allotropes are metastable in energy compared with that of graphene and, except for OPG-A and C3-10-H allotropes, the other phonon spectra of 18 selected allotropes are dynamically stable. In particular, the proposed C3-11 allotrope is energetically favorable than graphene when the temperature is increased up to 1043 K accord-ing to the derived free energies. The electronic band structures demonstrate that (ⅰ) the C3-8 allotrope is a semiconductor with an indirect DFT band gap of 1.04 eV, (ⅱ) another unusual allotrope is C3-12 which exhibits a highly fl at band just crossing the Fermi level, (ⅲ) four allotropes are Dirac semimetals with the appearance of Dirac cones at the Fermi level in the lattices without hexagonal symmetry, and (ⅵ) without the spin-orbit coupling (SOC) effect, the hexagonal C3-11 allotrope exhibits two Dirac cones at K and K’ points in its Brillouin zone in similarity with graphene.