[en] One-dimensional icosahedral boron chains and two-dimensional icosahedral boron sheets (icosahedral α, δ_6, and δ_4 sheets) that contain icosahedra B_1_2 as their building units have been predicted in a computer simulation study using a state-of-the-art semi-empirical Hamiltonian. These novel low-dimensional icosahedral structures exhibit interesting bonding and electronic properties. Specifically, the three-center, two-electron bonding between icosahedra B_1_2 of the boron bulk (rhombohedral boron) transforms into a two-center bonding in these new allotropes of boron sheets. In contrast to the previously reported stable buckled α and triangular boron monolayer sheets, these new allotropes of boron sheets form a planar network. Calculations of electronic density of states (DOS) reveal a semiconducting nature for both the icosahedral chain and the icosahedral δ_6 and δ_4 sheets, as well as a nearly gapless (or metallic-like) feature in the DOS for the icosahedral α sheet. The results for the energy barrier per atom between the icosahedral δ_6 and α sheets (0.17 eV), the icosahedral δ_6 and δ_4 sheets (0.38 eV), and the icosahedral α and δ_4 sheets (0.27 eV), as indicated in the respective parentheses, suggest that these new allotropes of boron sheets are relatively stable. (paper)