The electromagnetic response of silicon triangle nanoprisms in the near-infrared region is investigated. It is revealed that the bianisotropic dipole approximation is insufficient for this geometry since the direct application of the Onsager-Casimir symmetry rule to the dipole response leads to a contradictory conclusion. We show that to resolve this contradiction, it is necessary to take into account the nonlocal contributions of higher orders to the excited electric and magnetic dipole moments of the prisms. However, the inclusion in the consideration of nonlocal corrections to the dipole moments leads to the need to take into account the excitation of multipoles of a higher order than dipoles.