Complete scheme of four-dimensional crystallographic symmetry groups

  title={Complete scheme of four-dimensional crystallographic symmetry groups},
  author={A. F. Palistrant},
  journal={Crystallography Reports},
One of the main problems of four-dimensional geometric crystallography is considered; i.e., the complete scheme of four-dimensional crystallographic symmetry groups is presented, and the number of symmetry groups characterizing the 12 different categories entering this scheme is indicated for each of these categories. 

Spatio-temporal symmetry - crystallographic point groups with time translations and time inversion.

The crystallographic symmetry of time-periodic phenomena has been extended to include time inversion and one representative group from each of the 343 types has been tabulated.

Investigation of 5D point symmetry groups with an invariant 3D plane and immobile point on it

To reveal the structure of 5D point symmetry groups with an invariant 3D plane and immobile point on it, we review in detail the catalog of 1208 3D point groups of ten rosette P-symmetries at P ≅

Relativistic spacetime crystals

  • V. Gopalan
  • Physics
    Acta crystallographica. Section A, Foundations and advances
  • 2021
By appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown and hidden symmetries in relativist spacetime crystals are uncovered.



Three-dimensional point groups of hypercrystallographic second-order P-symmetries and their multidimensional applications

All the three-dimensional point groups of G30P 624 hypercrystallographic second-order P-symmetries have been derived at P ≃ G5430. On this basis, it was established that the category G87630 of

Finite rotation groups and crystal classes in four dimensions

  • A. C. Hurley
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1951
The groups of symmetries of three-dimensional lattices have been known for some time. They consist of finite rotation groups, the crystal classes, and infinite discrete motion groups, which include

Classification of symmetry groups

BROWN, P. J . (1956). Acts Cryst. 10, 133. Ctr~OTTI, P. & KKLP, G. R. (1959). Trans. Amer. Inst. Min. Met., Engrs. 215, 892. DAUBEN, C. H. & TEYIPLETON, D. H. (1955). Acta Cryst. 8, 841. FRLA_UF, J.