We report the first structural characterization of the triplet isomer of C6. Forty-one rovibrational/fine structure transitions in the nu 4(sigma u) antisymmetric stretch fundamental of the C6 cluster have been measured by diode laser absorption spectroscopy of a supersonic carbon cluster beam. The observed spectrum is characteristic of a centrosymmetric linear triplet state with cumulene-type bonding. The measured ground state rotational constant B0 = 0.048 479 (10)cm-1 and the effective bond length r(eff) = 1.2868 (1) angstroms are in good agreement with ab initio predictions for the linear triplet (3 sigma g-) state of C6.