The deposition of one silicon monolayer on the silver (111) substrate in the temperature range 150-300 °C gives rise to a mix of (4 × 4), (2√3 × 2√3)R30° and (√13 × √13)R13.9° superstructures which strongly depend on the substrate temperature. We deduced from a detailed analysis of the LEED patterns and the STM images that all these superstructures are given by a quasi-identical silicon single layer with a honeycomb structure (i.e. a silicene-like layer) with different rotations relative to the silver substrate. The morphologies of the STM images are explained from the position of the silicon atoms relative to the silver atoms. A complete analysis of all possible rotations of the silicene layer predicts also a (√7 × √7)R19.1° superstructure which has not been observed so far.