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Electric multipole ordering is a topic of interest because it is thought to be a promising mechanism of the so-called “hidden order.” The lanthanide compound CeB6 is a prototypical material exhibiting quadrupole ordering, i.e., electronic charge redistribution arising from the electron orbital degrees of freedom. Its ordered structure is believed to be an Oxy-type antiferroquadrupole (AFQ): more precisely, considering the local f-electron distribution, a CsCl-type cubic structure (space group: Pm3m) changes into a tetragonal structure (space group: I4/mmm) below the AFQ ordering temperature TQ = 3.3 K. This ordered structure has been primarily identified based on experiments under a finite magnetic field in the AFQ phase; however, the present study suggests that this may not be true under a zero field.Recently, we succeeded in observing the 11B-nuclear quadrupole resonance (NQR) signal of CeB6 near νQ= 560 kHz after years of struggle to observe it in the extremely low-frequency range. NQR is a resonance phenomenon between the energy levels of nuclear spin angular momentum, split by local Coulomb interactions between the nucleus and surrounding charges. Therefore, quadrupole ordering is expected to induce some anomalies in the NQR spectrum, such as a shift or split reflecting symmetry change. For the structure represented by I4/mmm, as the electrical environment differs for three crystallographically inequivalent B sites in a B6-octahedron, one expects to observe three distinguishable 11B-NQR signals. However, our experimental results presented no signs of spectral splitting, despite spectrum shift just below TQ, which is evidence of the AFQ order.We propose two possible interpretations of the results. In the first interpretation, basically within the framework of the Oxy-type structure, the AFQ moments dynamically fluctuate between the Oxy-, Oyz-, and Ozx-type orders, which may be tolerated because the crystal symmetry is still high in the zero field. If the fluctuations occur on a time scale much faster than 1/νQ~ 1.8 μs, the NQR analyses cannot differentiate between them. The second interpretation is that the real order in the zero-field region is different from the Oxy-type order. A promising structure is cubic Ia3, which belongs to the subgroups of Pm3m. In this structure, the Ce site with a three-fold rotation-inversion axis forms a triple-q AFQ order. Also there is a single B site, in accordance with the current results. Both proposals indicate unprecedented new states of order and may trigger a renewed interest in CeB6 research.(Written by T. Mito on behalf of all the authors.)"