The unique importance of the cyclopropenylidene molecule conveys significance to its low-lying isomers. Eleven low-lying electronic triplet stationary points as well as the two lowest singlet structures of C(3)H(2) have been systematically investigated. This research used coupled cluster (CC) methods with single and double excitations and perturbative triple excitations [CCSD(T)] and Dunning's correlation-consistent polarized valence cc-pVXZ (where X=D, T, and Q) basis sets. Geometries, dipole moments, vibrational frequencies, and associated infrared intensities of the targeted molecules have been predicted. The electronic ground state of cyclopropenylidene (3S, the global minimum) is the X (1)A(1) state with C(2v) point group symmetry. Among the 11 triplet stationary points, 7 structures are found to be minima, 2 structures to be transition states, and 2 structures to be higher-order saddle points. For the six lowest-lying triplet structures and singlet propadienylidene (2S), relative energies (zero-point vibrational energy corrected values in parentheses) with respect to the global minimum [ X (1)A(1) (3S)] at the cc-pVQZ-UCCSD(T) level of theory are predicted to be propynylidene (3)B(1aT)15.5(11.3)<propadienylidene[(1)A(1)(2S)]14.2(13.3)<propadienylidene[(3)B(1)(2T)]45.0(43.8)<cyclopropenylidene[(3)A(3aT)]53.8(52.5)<cyclopropyne[(3)B(2)(4aT)]70.0(70.6)<cyclopropenylidene [(3)B(1)(3cT)]71.2(69.9)<trans-propenediylidene [(3)A(")(5T)]73.6(70.7) kcal mol(-1). The combined energy for the [C((3)P)+C(2)H(2)(X (1)Sigma(g) (+))] system with respect to the global minimum (3S) is determined to be 107.4(103.8) kcal mol(-1). Therefore, these six triplet equilibrium structures are all energetically well below the dissociation limit to [C((3)P)+C(2)H(2)(X (1)Sigma(g) (+))].