Veysseyre, R, Weigel, D. and Phan, T. (2008) Crystal Families and Systems in Higher Dimensions, and Geometrical Symbols of Their Point Groups. I Cubic Families in Five Dimensional Space with Two, Three, Four and Six-Fold Symmetries. Acta Crystallographica Section A, 64, 675-686.

has been cited by the following article:

• TITLE: Crystallography in Spaces E2, E3, E4, E5 … Study of Three Crystal Families of Space E5

  AUTHORS: R. Veysseyre, D. Weigel, H. Veysseyre

  KEYWORDS: Crystallographic Point Groups, Isomorphism Classes, Hyper Cube and (di iso Hexagons)-al Crystal Families, Cubic and iso Cubic Point Groups

  JOURNAL NAME: Advances in Pure Mathematics, Vol.7 No.8, August 8, 2017

  ABSTRACT: In two previous papers, we explained the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes and we describe some crystal families. This paper mainly consists in the study of three crystal families of space E5, the (di-iso hexagons)-al, the hypercube 5 dim and the (hypercube 4 dim)-al crystal families. For each studied family, we explain their name, we describe their cell and we list their point groups which are classified into isomorphism classes. Then we give a WPV symbol to each group. (WPV means Weigel Phan Veysseyre). Our method is based on the description of the cell of the holohedry of each crystal family and of the results given by the Software established by one of us. The advantage to classify the point groups in isomorphism classes is to give their mathematical structures and to compare their WPV symbols. So the study of all crystal families of space E5 is completed. Some crystal families of space E5 can be used to describe di incommensurate structures and quasi crystals.