First-principles calculations are used to investigate ionicities of boron-boron bonds in B(12) icosahedra. It is observed that the geometrical symmetry breaking of B(12) icosahedra results in the spatial asymmetry of charge density on each boron-boron bond, and further in the ionicity of B(12) icosahedra. The results calculated by a new ionicity scale, a population ionicity scale, indicate that the maximum ionicity among those boron-boron bonds is larger than that of boron-nitrogen bonds in the III-V compound cubic BN. It is of great importance that such an ionicity concept can be extended to boron-rich solids and identical atom clusters.