Abstract The folding of the nucleosome array into a chromatin fiber modulates DNA accessibility and is therefore an important factor for the control of gene expression. The statistical analysis of the nucleosome repeat length in chromatin fibers reveals the presence of a ten-fold periodicity suggesting the existence of orientational constraints of the nucleosome units that provide the geometrical conditions of helical conformations. Recently, the elucidation of the x-ray crystal structure of a nucleosome tetramer array and the interpretation of electron microscopy images of reconstituted nucleosome arrays suggested two different architectures of the chromatin fiber. We approached the problem by integrating the experimental findings with geometrical, conformational and topological restraints, under the hypothesis of the minimum distortion of the nucleosome and linker DNA structures. We show that the excluded volume at linker crossing and the torsional energy limit the possible close packing of the nucleosomes in the chromatin fiber. In particular, the torsional energy of the chromatin fiber appears crucial in determining the kind of nucleosome packing for short nucleosome repeat lengths as in telomeres and yeast chromatin.