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Low-dimensional ferroelectric topological textures show abundant configurations such as flux-closure quadrants and vortices, suggesting potential applications in nano-electronic devices. However, the deterministic control of those polar textures is still challenging. By using piezoresponse force microscopy, threefold or fourfold vertex domain structures were observed in self-assembled BiFeO3 nano-islands, and the formation of such polar topological textures is strongly dependent on the size and shape of the nano-island. Furthermore, the vertex domain textures confined by geometry can be reversibly switched back and forth by external electric field, which are stabilized by the competition between elastic energy and electrostatic energy.