Diboron trioxide (B2O3) assumes critical importance as an effective oxidation inhibitor in prominent chemical applications. For instance, it has been extensively used in electrolysis and ceramic/glass technology. Results are presented of accurate quantum mechanical calculations using the PW1PW hybrid HF/DFT functional of four low-index surfaces of the low-pressure phase of B2O3: (101), (100), (011), and (001). Bond lengths, bond angles, and net Mulliken charges of the surface atoms are analyzed in detail. Total and projected density of states as well as surface energies are discussed. The occurrence of tetrahedral BO4 units on the lowest energy structures of two of these surfaces has been demonstrated for the first time. The corresponding surface orientations incur larger energies in reference to the two orientations featuring only BO3 units. All of the four investigated lowest energy structures have no dangling bonds, which reasonably relates to the experimentally observed low reactivity of this compound. Findings in this paper pave the way for potential interest in the perspective of future studies on the surfaces of amorphous B2O3, as well as on the hydroxylation of both crystalline and amorphous B2O3.