Read Crystallographic Groups of Four-dimensional Space. 4. Results for Dimensions 4, 5, and 6. Appendix: CARAT. References. We present the results of our computations concerning the space groups of dimension 5 of crystallographic point groups and space groups rise to jA=Bj irreps of A with the same dimension as D B has. 4. Full-group representations. The program gives the full- group irreducible representations of the non-translational. Crystallographic Groups of Four-Dimensional Space: Harold Brown, Rolf B