Among the multiple effects involved in chromatin condensation and decondensation processes, interactions between nucleosome core particles are suspected to play a crucial role. We analyze them in the absence of linker DNA and added proteins, after the self-assembly of isolated nucleosome core particles under controlled ionic conditions. We describe an original lamellar mesophase forming tubules on the mesoscopic scale. High resolution imaging of cryosections of vitrified samples reveals how nucleosome core particles stack on top of one another into columns which themselves align to form bilayers that repel one another through a solvent layer. We deduce from this structural organization how the particles interact through attractive interactions between top and bottom faces and lateral polar interactions that originate in the heterogeneous charge distribution at the surface of the particle. These interactions, at work under conditions comparable with those found in the living cell, should be of importance in the mechanisms governing chromatin compaction in vivo.