High-level ab initio methods are used to characterize nine isomers of C6H2 These include the thermodynamically favored triacetylene form and hexapentaenylidene. which is known to exist in the interstellar medium. Also included in the survey are three cyclic forms of tetradehydrobenzene and four additional structures that have not been investigated previously. Structures, dipole moments, parameters of rotational Hamiltonians, vibrational frequencies, intensities, and C-13 isotopic shifts are documented for all forms to assist efforts aimed at detecting these species in the laboratory. Perhaps the best candidate for detection in space is ethynylbutatriehylidene, which has a substantial dipole moment and a thermodynamic stability comparable to that of hexapentaenylidene. Notably, the symmetric disubstituted vinylidene isomer has a small and perhaps vanishing barrier to rearrangement.