The spin-1/2 low-dimensional quantum magnet antlerite, Cu3SO4(OH)4, is a natural mineral with a magnetic lattice consisting of three-leg ladders that are made of two nonequivalent Cu2+ ions with zigzag bonds. We synthesized large amounts of antlerite in the form of tiny single crystals, and we prepared much smaller deuterated crystals for the neutron diffraction experiment in order to determine the magnetic structure of the four different zero-field magnetic phases that were so far reported: α1, α2, I1 and I2. The main goal of the proposed experiment is to verify the magnetic origin of the observed diffuse signal, distinguish it from nonmagnetic background using polarized neutrons, and outline its region of presence in momentum space and in temperature