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We present experimental (a), theoretical (b-c) and computer simulations (d) findings about nematic phases arising in liquid crystals composed of polar molecules. The origin of proper and improper ferroelectricity is attributed to specific symmetries of molecular pair interaction [1]. M1 is paraelectric, MP is proper ferroelectric [2-3], and M2 is intermediate improper splay antiferroelectric [4] consisting of cylindrical domains. Non-polar S and polar P order parameters vary along r; P changes sign between the neighboring cylinders [red and green in (d)]. Local polarization in M2 is higher than in MP; average P is equal to zero in M2 and different from zero in MP.