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We perform ab initio structure-prediction calculations of the low-energy crystal structures of two-dimensional silicon. Besides the well-known silicene and a few other allotropes proposed earlier in the literature, we discover a wealth of new phases with interesting properties. In particular, we find that the ground state of two-dimensional silicon is an unreported structure formed by a honeycomb lattice with dumbbell atoms arranged in a zigzag pattern. This material, that we call zigzag dumbbell silicene, is 218 meV/atom more stable than silicene and displays a quasi-direct band gap of around 1.11 eV, with a very dispersive electron band. These properties should make it easier to synthesize than silicene and interesting for a wealth of opto-electronic applications.