An intriguing structural transition from the quasi-planar form of B12 cluster upon the interaction with lithium atoms is reported. High-level computations show that the lowest energy structures of LiB12, Li2B12, and Li3B12 have quasi-planar (Cs), tubular (D6d), and cage-like (Cs) geometries, respectively. The energetic cost of distorting the B12 quasi-planar fragment is overcompensated by an enhanced electrostatic interaction between the Li cations and the tubular or cage-like B12 fragments, which is the main reason of such drastic structural changes, resulting in the smallest tubular (Li2B12) and cage-like (Li3B12) boron structures reported to date.