$\alpha$-T form does not exist and that the structure is stabilized only by inclusion of foreign atoms.

In the 2000’s, nanostructures were repeatedly reported to have the structure of pure $\alpha$-T boron.[@Zhang02; @Wang03; @Xu04; @Yang04; @Kirihara05] Hayami and Otani explained the existence of pure $\alpha$-T boron in nanostructures by the presence of low surface energies.[@Hayami08] Subsequently, they predicted the possibility of pure $\alpha$-T boron bulk structures with the composition B$_{52}$.[@Hayami10] After this theoretical work, the high-pressure syntheses of bulk $\alpha$-T boron were reported by several groups [@Ekimov11; @Ekimov11a; @Qin12; @Kurakevych12; @Kurakevych13; @Solozhenko13]. Notwithstanding the prediction by Hayami and Otani, many different forms of tetragonal boron were discovered, including a known form of $\beta$-tetragonal boron [@Ma03]. The current situation occurs to be rather complicated and many questions are raised: Does pure $\alpha$-T boron truly exists? And if it does, what stabilizes its structure and what was wrong with the previous theory? The purpose of this paper is to answer these questions.

To say it shortly, the qualitative argument of Longuet-Higgins and Roberts is not wrong. The structure of B$_{50}$ is indeed not stable. However, there are ingenious ways to circumvent this instability.[@Shirai12] One way is a deviation from stoichiometry. A suitable 