Single crystals of the so-called β-tetragonal (or tetragonal II or III) boron modification have been obtained from boron deposits prepared by hydrogen reduction of BBr 3 on tantalum filaments at 1200°C. Chemical analysis of the samples shows that this phase can be regarded as a true modification of pure elemental boron in contrast to α-tetragonal phases which require small amounts of foreign atoms to stabilize their boron framework. The lattice parameters ( a = 10.14(1)Å; c = 14.17(1)Å) were obtained and refined from single crystal data. The unit cell contains four chemical units, B 21 · 2B 12 · B 2.5 resulting in dc = 2.34 g cm -3 ( dm = 2.36(2) g cm -3). The systematic extinctions are compatible with space group P4 1 or P4 3. The structure was determined from 1009 independent reflexions using a model derived from the recently solved structure of α - AlB 12 ( a = 10.161Å; c = 14.283Å; space group P4 12 12 or P4 32 12). The final R value (unweighted data) is 9.6%. Basically, the structure of this tetragonal form of boron consists of the same three-dimensional boron skeleton, built upon simple and twinned icosahedra, as that of α-AlB 12. However, the defective twinned icosahedral B 19 units in α-AlB 12 are now completed (B 21 units) in the related tetragonal boron. A number of interstitial sites, located at positions different from those occupied by aluminum in α-AlB 12, are totally or partially filled by boron atoms and very probably increase the stability of the boron framework.