Potential energy surfaces of anionic B6Hy clusters were sampled using the coalescence kick method. We found that the planar to three-dimensional transition occurs in this system when y = 4. This is an important discovery because this transition suggests a major structural change as a function of dehydrogenation for the stoichiometric BnHn- polyhedral boranes. We also found that the B6H3- global minimum structure has an optical isomer. The chemical bonding patterns revealed by the adaptive natural density partitioning (AdNDP) analysis explain the geometric structure of all clusters presented here. From our chemical bonding analysis, we concluded that the 2D-3D transition occurs at B6H4- because the addition of one extra hydrogen atom further destroys the network of the peripheral 2c-2e B-B sigma-bonding, making planar structures less stable, and because the distorted octahedral structure provides some occupation of all sand p-AOs of boron, avoiding the presence of any empty atomic orbitals. Theoretical vertical electron detachment energies (VDEs) were calculated for comparison with future experimental work.