Share This Article:

Crystallography in the Spaces E2, E3, E4, E5 ...N0II Isomorphism Classes and Study of Five Crystal Families of Space E5

Abstract Full-Text HTML Download Download as PDF (Size:527KB) PP. 196-207
DOI: 10.4236/apm.2015.54021    2,169 Downloads   2,549 Views   Citations

ABSTRACT

In the paper N0II, we describe some isomorphism classes and we apply their properties to the study of five crystal families of space E5. The names of these families are the following ones (monoclinic di iso squares)-al, decadic-al, (monoclinic di iso hexagons)-al, (rhombotopic cosa=-1/4)-al and rhombotopic cosa=-1/5. The meaning of these names will be given in Paragraphs 5 and 6 with some geometric properties of their cell.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Veysseyre, R. , Weigel, D. , Phan, T. and Veysseyre, H. (2015) Crystallography in the Spaces E2, E3, E4, E5 ...N0II Isomorphism Classes and Study of Five Crystal Families of Space E5. Advances in Pure Mathematics, 5, 196-207. doi: 10.4236/apm.2015.54021.

References

[1] Veysseyre, R., Weigel, D. and Phan, T. (1993) Crystallography, Geometry and Physics in Higher Dimensions. XI. A New Geometrical Method for Systematic Construction of the n-Dimensional Crystal Families: Reducible and Irreducible Crystal Families. Acta Crystallographica Section A, 49, 481-486.
http://dx.doi.org/10.1107/S0108767392011024
[2] Phan, T., Veysseyre, R. and Weigel, D. (1988) Crystallography, Geometry and Physics in Higher Dimensions. IV. Crystallographic Cells and Polytopes or “Molecules” of Four-Dimensional Space E4. Acta Crystallographica Section A, 44, 627-637.
http://dx.doi.org/10.1107/S0108767388003009
[3] Coxeter, H.S.M. (1973) Regular Polytopes. Dover, New York.
[4] Veysseyre, R. and Veysseyre, H. (2002) Crystallographic Point Groups of Five-Dimensional Space 1. Their Elements and Their Subgroups. Acta Crystallographica Section A, 58, 429-433.
[5] Weigel, D., Phan T. and Veysseyre, R. (2008) Crystal Families and Systems in Higher Dimensions, and Geometrical Symbols of Their Point Groups. II Cubic Families in Five and n-Dimensional Spaces. Acta Crystallographica Section A, 64, 687-697.
[6] Janssen, T., Birman, J.L., Koptsik, V.A., Senechal, M., Weigel, D., Yamamoto, A., Abrahams, S.C. and Hahn, T. (1999) Symmetry Elements in Space Groups and Point Groups. Acta Crystallographica Section A, 55, 761-782.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.