Quantitative X-ray diffraction techniques have been used to determine the atomic structures of the ∑ = 5 and 13 [001] twist boundaries in Au with a resolution of 0.09 Å or better. The reciprocal lattices of these boundaries were mapped out using synchrotron radiation. The atomic structures were obtained by testing model structures against the intensity observations with a chi square analysis. The boundary structures were modeled using polyhedra, including octahedra, special configurations of tetrahedra and Archimedian anti-prisms, interwoven together by the boundary symmetry. The results of this work point to the possibility of obtaining general rules for grain boundary structures based on X-ray diffraction observations that give the atomic positions with high resolution.