: A comparison of hypothetical (theoretically considered) and real structures of boron-rich solids. For most systems theory was unable to correctly predict their semiconducting properties (second column). The experimentally determined electronic properties are given in the last column. For the real structures, some ground-state properties are indicated, such as high- or low-symmetry (H-Sym./L-Sym.) and stoichiometric or non-stoichiometric compositions (St./NSt.). The experimentally determined electronic properties are given in the last column. $N_{\rm at}$ is the number of atoms per unit cell. Odd numbers of electrons $N_{\rm el}$ are indicated by italicized numbers. The last entry of this table contains our conclusion about the structure of $\alpha$-T boron, that is presented in this article.[]{data-label="tbl:stoichiometry"}

It is well known that boron-based materials are characterized as [*electron deficient*]{} systems in the chemical literature.[@Pauling] Electron deficiency and the metal/insulator problem occur unrelated and therefore we had not be aware until recently that these two different matters are actually intimately related. In the last decade, the effect of POS was extensively studied by DFT calculations on $\beta$-R boron.[@Masago06; @Setten07; @Widom08; @Ogitsu09] It was found that the occupation of IS in boron-rich solids cannot be considered as defects, contrary to the usual notion in the literature about 