The precise number of base pairs per turn of the DNA double helix in the nucleosome core particle has been the subject of controversy. In this paper the positions of nuclease cutting sites are analysed in three dimensions. Using this midpoint of the DNA on the nucleosome dyad as origin, the cutting site locations measured along a strand of DNA are mapped onto models of the nucleosome core containing DNA of different helical periodicities. It is found that a helical periodicity of 10.5 base pairs per turn leads to cutting site positions which are sterically inaccessible. In contrast, a periodicity of 10.0 base pairs per turn leads to cutting site positions which are not only sterically sound, but which fall into a pattern such as would be expected when the access of the nuclease to the DNA is restricted by the presence of the histone core on one side and of the adjacent superhelical turn of DNA on the other. As proposed earlier by us (1), a value for the helical periodicity close to 10 base pairs per turn on the nucleosome, taken together with a periodicity close to 10.5 for DNA in solution - a value now established - resolves the so-called linkage number paradox.