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Crystallography in the Spaces E<sup>2</sup>, E<sup>3</sup>, E<sup>4</sup>, E<sup>5</sup> ...N<sup>0</sup>II Isomorphism Classes and Study of Five Crystal Families of Space E<sup>5</sup>
Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
Institut Supérieur de Mécanique de Paris, Paris, France
- 1 Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
- 2 Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
- 3 Laboratoire Mathématiques appliquées aux Systèmes, Ecole Centrale Paris, Paris, France
- 4 Institut Supérieur de Mécanique de Paris, Paris, France
Advances in Pure Mathematics·Volume 05 (2015)·Pages 196–207·Published 20 March 2015·DOI10.4236/apm.2015.54021
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Abstract
In the paper N 0 II, we describe some isomorphism classes and we apply their properties to the study of five crystal families of space E 5 . The names of these families are the following ones (monoclinic di iso squares)-al, decadic-al, (monoclinic di iso hexagons)-al, (rhombotopic cos a =-1/4 )-al and rhombotopic cos a =-1/5 . The meaning of these names will be given in Paragraphs 5 and 6 with some geometric properties of their cell.
KeywordsCrystal Families of Space E<sup>5</sup>NamesPoint Groups of the FamiliesRhombotopic Crystal Families
- 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
- 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
- Coxeter, H.S.M. (1973) Regular Polytopes. Dover, New York.
- 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.
- 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.
- 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.