The effect of removing two protons, hydrogen atoms, or hydrides from the stable icosahedral B12H122- is investigated theoretically. The resulting B12H10q (q = 4-, 2-, 0) isomers show interesting and understandable bond distance and stability variations, as well as special deformations associated with the apex-ring configuration typical of the underlying polyhedron. The dianions are analogous to o-, m-, and p-benzyne and have the special feature of distinct singlet and triplet states not far removed from each other in energy.