We predict three new polymorphs of boron by applying density functional theory (PBE flavor) to large shear deformations starting from the recently discovered γ-B28 boron phase (stable above 9 GPa and 1000 K). We find that continuous deformation along the (100)/⟨001⟩ slip system leads to two new phases, named here as γ-B12-(B2)6 and γ-B12-(B···B)6. We show that these γ-B12-(B2)6 and γ-B12-(B···B)6 phases can also be obtained from uniaxial tensile and compressive deformations of the γ-B28 phase along the ⟨101⟩ direction, respectively. However, the reverse compressive loading on the newly formed γ-B12-(B2)6 phase transforms it to itself, not the γ-B28 phase, because of the transferability of the three-center two-electron bond under deformation. This makes the new phase γ-B12-(B2)6 a special type of superelastic material. In addition, application of reverse tensile deformation on the newly formed γ-B12-(B···B)6 phase, transforms it to a third new phase, named α-B12-BB, that is metallic, suggesting increased ductility that might make α-B12-BB important for applications in electronic devices. We compared the structural character, mechanical properties, and electronic properties of these new phases to each other and to other phases of boron. We show that the three new phases are dynamically stable at zero pressure. These results show how modifying the connections between boron icosahedra using one to two atom chains can lead to dramatically different mechanical and electronic properties.