Assemblage compact d'hypersphères identiques à n dimensions

The crystallographer's main problem (i. e. the phasing of Fourier transform moduli) leads to the study of n-sphere periodic close packing. The geometric properties of this arrangement allow one to determine by recurrence reasoning the matrix of the general expressions for the coordinates of the points that define the cell. It is therefore easy to deduce the cell volume and the packing ratio of the unique hypersphere which is by hypothesis present in the cell. A numerical study of these expressions makes it possible to point out that 'paradoxically' this n-sphere fills only a negligible volume of the primitive cell and that this volume becomes less as the dimension n of the space increases.