Direct and quantitative determination of the orbital ordering in

Results of non-resonant X-ray Bragg diffraction by $\chem{CeB_6}$ are reported. This material has been described in terms of a simple antiferro-quadrupolar order below $T_{\ab{Q}}=3.2$$\un{K}$. We determine for the first time, directly and quantitatively the orbital ordering in this material. In particular, we find direct evidence for a simultaneous ordering of a quadrupole (QP) and a hexadecapole (HDP) moments below $T_{\ab{Q}}$. From a strong dependence of the Bragg intensity on applied magnetic field in phase II, we conclude that octupole (OP) moments are induced and are coupled to the QP and HDP moments. When spontaneous magnetic dipole order sets in below $T_{\ab{N}}=2.4$$\un{K}$ (phase III), a large enhancement of the Bragg intensity confirms the coupling between the dipole and the QP, OP and HDP moments