The trigonal strain-relief pattern formed by an Ag bilayer on Pt(111) is a prominent example for dislocation networks and their use as nanotemplates. However, its atomic structure has not been solved. Combining scanning tunneling microscopy, low-energy ion scattering, and x-ray photoelectron diffraction, we demonstrate that, unexpectedly, about 22% of the atoms exchange across the Ag/Pt interface, and that the partial dislocations defining the trigonal network are buried in the Pt interface layer. We present an embedded-atom-method simulation identifying the lowest energy structure compatible with all experimental findings.