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.