The structures and energetics of Li(6) (+), Li(6) (-) and three isomers of Li(6) are investigated using the coupled-cluster singles, doubles and perturbative triples [CCSD(T)] method with valence and core-valence correlation consistent basis sets of double- to quadruple-zeta quality (cc-pVXZ and cc-pCVXZ, where X=D-Q). These results are compared with qualitatively different predictions by less reliable methods. Our results conclusively show that the D(4h) isomer is the global minimum structure for Li(6). It is energetically favored over the C(5v) and D(3h) structures by about 5.1 and 7.1 kcal mol(-1), respectively, after the inclusion of the zero-point vibrational energy (ZPVE) correction. Our most accurate total atomization energies are 123.2, 117.6, and 115.7 kcal mol(-1) for the D(4h), C(5v), and D(3h) isomers, respectively. Comparison of experimental optical absorption spectra with our computed electronic spectra also indicate that the D(4h) isomer is indeed the most stable structure. The cation, anion, and some higher spin states are investigated using the less expensive cc-pCVDZ basis set. Adiabatic ionization energies and electron affinities are reported and compared with experimental values. Predictions of molecular properties are found to be sensitive to the basis set used and to the treatment of electron correlation.