Magnetic susceptibility anisotropy and high sensitivity magnetostriction measurements are used to investigate the symmetry of CeB6 ordered states. The antiferromagnetic state is confirmed as tetragonal, but no deviation from the cubic symmetry is observed in the so-called antiferroquadrupolar phase, where only volume effects are detected. In this phase, the temperature dependence of the strain field-susceptibilities is typical of non-ordered quadrupoles. Moreover, while an antiferroquadruplar order should be cubic, this symmetry is incompatible with the 1 2 1 2 1 2 ordering wave-vector. The antiferroquadrupolar description of CeB6 phase II is clearly inconsistent and an alternative model, based on a unidimensional representation of the cube, has to be sought for.In rare-earth compounds, the degrees of freedom of the 4f ions are collectively involved at low temperature to form ordered states. The most common kind of order is the magnetic one that exists in a number of varieties. The orbital order is a less common situation, where only the orbital degeneracy of the 4f ion is involved, without the stabilization of magnetic moments. It requires the orbital degeneracy to survive the crystal-field effect, which means the 4f ions sites are of high symmetry. As the highest symmetry is that of the octaedra, cubic systems are the most favorable scene for the development of orbital related effects [1]. There, the lifting of the degeneracy is equivalent to the emergence of 4f electric quadrupole moments and the associated order are referred to as "quadrupolar". By analogy with the ferromagnetism, the order that doesn't change the crystal periodicity is called ferroquadrupolar. One can also consider a state where the 4f quadrupoles are changing from site to site, thus defining an "antiferroquadrupolar" order (AFQ), analog to the antiferromagnetism. For more than two decades, the most cited example of such an antiferroquadrupolar order has been CeB 6 phase II. This system crystallizes within the CaB 6 -type structure and displays complex magnetic phase diagrams [2,3]. CeB 6 orders antiferromagnetically at T N = 2.4 K (phase III) and its most intriguing feature is the occurrence of a non-magnetic state (phase II) below T Q = 3.2 K, before entering the paramagnetic state (phase I). In phase II, a magnetic field induced Facing such inconsistencies and a confusing mass of experimental data, we thought that a crucial clarification would come from an accurate investigation of phase II symmetry. This can be achieved from macroscopic experiments on a single crystal. For a rare-earth based system, magnetic measurements are first to consider. In cubic crystals, an accurate determination of the first-order magnetic susceptibility can reveal a symmetry lowering : any deviation from the cubic symmetry will result in an anisotropic susceptibility. Due to the magnetoelastic coupling, the lattice necessarily reflects a symmetry lowering. The detection of the associated strain can be very sensitive, capacitance dilatometer being able to detec...