The six-vertex cobalt carbonyl clusters [Co6C(Co)(n)](2-) (n = 12, 13, 14, 15, 16) with an interstitial carbon atom have been studied by density functional theory (DFT). These DFT studies indicate that the experimentally known structure of [Co6C(CO)15](2-) consisting of a Co-6 trigonal prism with each of its edges bridged by carbonyl groups is a particularly stable structure lying more than 20 kcal/mol below any other [Co6C(CO)(15)](2-) structure. Addition of a CO group to this [Co6C(CO)(15)](2-) structure gives the lowest energy [Co6C(CO)(16)](2-) structure, also a Co-6 trigonal prism with one of the vertical edges bridged by two CO groups and the remaining eight edges each bridged by a single CO group. However, this [Co6C(CO)(16)](2-) structure is thermodynamically unstable with respect to CO loss reverting to the stable trigonal prismatic [Co6C(CO)(15)](2-). This suggests that 15 carbonyl groups is the maximum that can be attached to a Co6C skeleton in a stable compound. The lowest energy structure of [Co6C(CO)(14)](2-) has a highly distorted octahedral Co-6 skeleton and is thermodynamically unstable with respect to disproportionation to [Co6C(CO)(15)](2-)and [Co6C(CO)(13)](2-). The lowest energy [Co6C(CO)(13)](2-) structure is very similar to a known stable structure with an octahedral Co-6 skeleton. The lowest energy [Co6C(CO)(12)](2-) structure is a relatively symmetrical D-3d structure containing a carbon-centered Co-6 puckered hexagon in the chair form.