  High-quality single crystals of LuB12 are grown using the induction zone
melting method. The X-ray data are collected at temperatures 293, 135, 95, 50
K. The crystal structure of LuB12 can be refined with record low R-factor in
the cubic Fm-3m symmetry group despite reiterated observations of the cubic
symmetry distortions both in the unit-cell values and in the physical
properties. A peculiar computing strategy is developed to resolve this
contradiction. True symmetry of the electron-density distribution in LuB12 is
proved to be much lower than cubic as a result, which correlates very
accurately with anisotropy of transport properties of LuB12.
