The deposition of one silicon monolayer on Ag(1 1 1) gives rise to a set of superstructures depending on growth conditions. These superstructures are correlated to the epitaxy between the honeycomb structure of silicon (so called silicene) and the silver substrate. In this paper, from a detailed re-analysis of experimental results, obtained by scanning tunneling microscopy and by low energy electron diffraction on the (2√3 × 2√3)R30° structure, we propose a new atomic model of the silicene layer based on periodic arrangements of perfect areas of (2√3 × 2√3)R30° surrounded by defect areas. A generalization of this model explains the main experimental observations: deviation of the average direction, Moiré patterns and apparent global disorder. In the frame of the proposed model, the apparent disorders observed on the STM images, would be topological effects, i.e. the silicene would keep a quasi-perfect honeycomb structure.