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. Strain-relief patterns formed by heteroepitaxial films act as templates for the self-assembly of highly ordered nanostructure superlattices. 1 The first system where the growth kinetics has been studied is a superlattice of Ag islands grown on a trigonal network (TN) formed by two monolayers (ML) of Ag/Pt(111). 2,3 The system has been modeled by assuming a network of surface Shockley partial dislocations 4 acting as repulsive line defects and thus confining the deposited Ag adatoms into the (25 × 25) unit cells. 2,3 However, the topmost Ag layer of the TN has recently been shown to be nearly perfectly hexagonal; hence there are no partial dislocations at the surface. 5,6 Nevertheless, the TN exhibits remarkable template functions. Well-ordered sputter holes 5 and adsorbed organic molecules, 6-8 as well as strong spatial variations of the local work function 9 have been reported. A fundamental understanding of any template function evidently requires knowledge of its atomic structure. 10 Despite considerable efforts, a realistic atomistic model has not yet been developed for the 2 ML Ag/Pt(111) TN.Silver on Pt(111) is a system with a particularly rich surface phase diagram. Submonolayers deposited at room temperature (RT) are pseudomorphic for islands smaller than 20 nm, whereas larger islands form surface partial dislocations. 11,12 Counterintuitively, the dislocations disappear at a full monolayer (defined as one Ag atom per Pt substrate atom), where the stress resulting from the misfit is largest. This has been related to the chemical adatom potential and to the presence of an adatom gas. 11 Further growth at RT leads to a striped phase (SP) 4,13 with pairs of partial dislocations. Upon annealing to 800 K the SP transforms into the stable TN structure. 4 Deposition of Ag submonolayers at higher temperature, or their annealing at T > 620 K, leads to a real mixture formed by monolayer Ag clusters embedded into the uppermost atomic substrate layer for a coverage < 0.5 ML and the reverse for 0.5 ML < < 1.0 ML. 14 This mixing has been confirmed by CO titration 15 and He-atom scattering 16 and is confined to the uppermost layer; hence, the name "surface alloy". 17 For 1.0 ML, especially for = 2 ML, Ag and Pt were believed to be phase separated up to the Ag desorption temperature.In this paper we report the surprising observation that the system mixes again for 2 ML Ag in the TN structure. This mi...