We report neutron diffraction studies of the magnetic structure in BaTiOCu4(PO4)4 , which is a newly discovered magneticinsulator crystallizing in a tetragonal chiral crystal structure with P4212 space group [1]. The crystal structure ischaracterized by an antiferro-rotative arrangement of Cu4O12 square cupola clusters formed by four corner sharing CuO4plaquettes. Below 9.5 K these magnetic clusters order in a complex noncollinear magnetic structure which can be describedby an antiferroic order of magnetic quadrupole moments on Cu4O12 square cupolas.The magnetic transition is accompanied by a magnetic-field-induced peak in dielectric constant divergent toward T = 9.5 K,indicative of an onset of field-induced antiferroelectric order [2]. To the best of our knowledge, this is the first experimentalobservation of the magnetoelectric-activity due to magnetic quadrupole moments [3], which opens the arena for furtherstudies of this and related compounds.In this presentation, we shall focus on the determination of the magnetic structure exploiting a combination of powderneutron diffraction and so-called spherical neutron polarimetry. The powder diffraction measurement was able to identify twopossible models for the magnetic structure, as depicted in the figure. Both structures are noncollinear, but differ by havingthe moments either in or out of the CuO4 planes. Powder diffraction could only provide limited discrimination between thetwo models. Spherical neutron polarimetry is a convenient, albeit rarely used tool for understanding complex magneticstructures which often can provide unambiguous solutions to withstanding problems. In this case spherical neutronpolarimetry unambiguously identifies structure (b) with the moments pointing out of the CuO4 planes.