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We investigate tunable electric polarization and electronic structure of quasi-two-dimensional (quasi-2D) allotropes of selenium, which are formed from their constituent one-dimensional (1D) structures through an inter-chain interaction facilitated by the multi-valence nature of Se. Our em ab initio calculations reveal that different quasi-2D Se allotropes display different types of electric polarization, including ferroelectric (FE) polarization normal to the chain direction in alpha and delta allotropes, non-collinear ferrielectric (FiE) polarization along the chain axis in tau-Se, and anti-ferroelectric (AFE) polarization in eta-Se. The magnitude and direction of the polarization can be changed by a previously unexplored rotation of the constituent chains. In that case, an in-plane polarization direction may change to out-of-plane in alpha-Se and delta-Se, flip its direction, and even disappear in tau-Se. Also, the band gap may be reduced and changed from indirect to direct by rotating the constituent chains about their axes in these quasi-2D Se allotropes.