How can boron form bonds with three or four neighboring atoms?

Boron forms bonds with three or four neighboring atoms through the process of hybridization, which allows it to accommodate its valence electrons into different geometric configurations.1

Because the energy required to remove three electrons to form a $B^{3+}$ ion is prohibitively high, boron consistently forms covalently bonded compounds. To facilitate this, one of boron's $2s$ electrons is promoted to a $2p$ orbital, resulting in an outer electron configuration of $2s^{1}2p^2$. These orbitals can then be mixed to form:12

• $s{p}^2$ Hybridization: This configuration allows boron to form bonds with three other atoms, resulting in planar molecules such as borazine or halides like boron trifluoride.12
• $s{p}^3$ Hybridization: This configuration allows boron to be four-coordinated, with the four groups disposed tetrahedrally around the atom. This typically occurs in metal borohydrides or when three-coordinated boron molecules act as Lewis acids to accept an unshared pair of electrons from a donor atom.12