Crystallographic point groups in five dimensions

Abstract

AbstractThis paper describes an approach to the deduction and labeling of crystallographic point groups in n-dimensional spaces where n is an odd number. It shows that point groups in such spaces may be formed from the generators of rotational groups and a single inversion operation characteristic of the odd dimension. Results are given for 188 of the 955 crystallographic point groups in a five dimensional space and the extension to the remainder of the groups is made clear. Since 3 is an odd number, the 32 classical point groups are used to illustrate the use of generators for this purpose. Further extensions to seven dimensions and to even dimensions are then discussed.