We propose a unified mechanism of phase transitions in the high density solutions of Nucleosomal Core Particles. We demonstrate its relation with the high shape and charge anisotropy of the NCP due to the DNA wrapping around the histone protein core. Hexagonal-to-lantellar transition in the solution of NCP columnar aggregates is shown to be driven by the condensation of the periodic antiparallel polar vector field. The transition results in the polar dyadic axes correlations. Fine structure of the NCP organization is also explained, namely the correlated tilting of NCP with respect to the column axis.