We provide a first-principles, materials-specific theory of multipolar order and superexchange in NpO2 by means of a noncollinear local-density approximation +U (LDA+U) method. Our calculations offer a precise microscopic description of the triple-q antiferro ordered phase in the absence of any dipolar moment. We find that, while the most common nondipolar degrees of freedom (e.g., electric quadrupoles and magnetic octupoles) are active in the ordered phase, both the usually neglected higher-order multipoles (electric hexadecapoles and magnetic triakontadipoles) have at least an equally significant effect. ; JRC.E.6-Actinides research