%0 Journal Article
%T Crystallography in Spaces E<sup>2</sup>, E<sup>3</sup>, E<sup>4</sup>, E<sup>5</sup> ...N<sup>0</sup>I Isomorphism Classes: Properties and Applications to the Study of Incommensurate Phase Structures, Molecular Symmetry Groups and Crystal Families of Space E<sup>5</sup
%A R. Veysseyre
%A D. Weigel
%A T. Phan
%A H. Veysseyre
%J Advances in Pure Mathematics
%P 137-149
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.54017
%X This paper mainly consists of the classification of
all crystallographic point groups of n-dimensional space with n ¡Ü 6 into
different isomorphism classes. An isomorphism class is defined by a type of
finite mathematic group; for instance, the different types of mathematic groups
have been well defined and studied by Coxeter. This classification may be used
in the investigation of several domains of crystallography such as the study of
the incommensurate phases, the quasi crystals ¡ Indeed, each mathematic substitution group characterizes an isomorphism
class of crystallographic point groups (spaces E2 or E3),
of point groups of super crystals (spaces E4 or E5), and of
molecular symmetry groups (spaces E2 or E3). This
mathematic group gives interesting information about: 1) the incommensurate phase structures and their
phase transitions according to the Landau¡¯s theory in their super spaces
E