[*metal/insulator*]{} problem. Table \[tbl:stoichiometry\] summarizes this discrepancy. This table is adapted from a paper of R. Schmechel and H. Werheit [@Schmechel99], who first pointed out the importance of deviation from stoichiometry for the metal/insulator problem. The last entry of the table corresponds to $\alpha$-T boron, where for convenience the conclusion of this study is already given. We can notice in this table that, whenever the metal/insulator problem occurs, deviation from stoichiometry is observed. In boron-rich solids, the crystals are composed of a regular arrangement of icosahedra and various kinds of atoms at interstitial sites. Those interstitial sites are either fully occupied sites (FOS) or partially occupied sites (POS). The deviation from stoichiometry is a result of the presence of POS.

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         Crystal                                                                                                             
                             Sym.        $N_{\rm at}$   $N_{\rm el}$  Prediction    $N_{\rm at}$        Ground state           Elect.
     $\alpha$-rhomb.     $D_{\rm 3d}$              12             36   semicon.               12           H-sym.             semicon.
                                                                                                             St.             
     $\beta$-rhomb.      $D_{\rm 3d}$             105      [*315*]{}    metal              106.5           L-sym.             semicon.
                                                                                                            NSt.             
   ${\rm B_{13}C_{2}}$   $D_{\rm 3d}$              15       [*47*]{}    metal                 15           L-sym.             semicon.
                                                                                    (on average)            NSt.             
     $\alpha$-tetra.     $D_{\rm 4h}$              50            150    metal        52+$\delta$    $\delta=0$ for $T=0$      semicon.
                                                   52            156   semicon.                   $\delta \neq 0$ for $T>0$  
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