The concentration of carriers in LuB 12 is evaluated theoretically by applying ab initio FP-LMTO calculations. Theoretical results are found to be in agreement with high precision measurements of the Hall R H (T) coefficient which were carried out on single crystals of the rare earth dodecaborides RB 12 (R = Ho, Er, Tm, Lu) at temperatures 1.8-300 K. A nature of the antiferromagnetic ordering in RB 12 is investigated within the RKKY-like model, which was supplemented by comprehensive electronic structure calculations for paramagnetic, ferromagnetic and antiferromagnetic phases. Though a number of experimental and theoretical investigations were carried out for RB 12 [1,[5][6][7][8][9], the mechanisms of microscopic magnetic interactions, as well as fine details of the electronic structure in these compounds, are still not clear.In order to elucidate the origin of principal interactions and electronic states responsible for magnetic ordering in RB 12 , the high precision measurements of the Hall resistivity r H (j, T, H) were carried out for HoB 12 , ErB 12 , TmB 12 and LuB 12 compounds within a wide temperature range of 1.8-300 K in magnetic fields up to 80 kOe [6,7].Based on the measured Hall coefficients of RB 12 [6,7], the corresponding values of normalized charge carrier concentration n/n 4f = (R H en 4f ) -1 are evaluated and presented in Fig. 1. Here n and n 4f are the numbers of carriers and rare earth atoms per the primitive cell correspondingly and R H is the Hall coefficient. As can be seen in Fig. 1, the temperature dependences of the charge carrier concentration are distinct from each other for the nonmagnetic LuB 12 and magnetic dodecaborides. In particular, a pronounced anomaly of n/n 4f (T) is revealed in LuB 12 at T* » 56 K, whereas magnetic compounds HoB 12 , ErB 12 and TmB 12 demonstrate a weak enough variation of the carrier concentration n at intermediate temperatures. Indeed, on the average, the n/n 4f value is varied within about 10% through the paramagnetic region of RB 12 series, namely 2.0-2.2. It should be stressed that this result contradicts to the assumption that the conduction band in RB 12 compounds is formed by only one 5d electron of a rare earth element [10]. To shed