We present a complete formulation of the two-dimensional and three-dimensional crystallographic space groups in the conformal geometric algebra of Euclidean space. This enables a simple new representation of translational and orthogonal symmetries in a multiplicative group of versors. The generators of each group are constructed directly from a basis of lattice vectors that define its crystal class. A new system of space group symbols enables one to unambiguously write down all generators of a given space group directly from its symbol.
%0 Journal Article
%1 :/content/aip/journal/jmp/48/2/10.1063/1.2426416
%A Hestenes, David
%A Holt, Jeremy W.
%D 2007
%J Journal of Mathematical Physics
%K geometricalgebra
%N 2
%P -
%R http://dx.doi.org/10.1063/1.2426416
%T Crystallographic space groups in geometric algebra
%U http://scitation.aip.org/content/aip/journal/jmp/48/2/10.1063/1.2426416
%V 48
%X We present a complete formulation of the two-dimensional and three-dimensional crystallographic space groups in the conformal geometric algebra of Euclidean space. This enables a simple new representation of translational and orthogonal symmetries in a multiplicative group of versors. The generators of each group are constructed directly from a basis of lattice vectors that define its crystal class. A new system of space group symbols enables one to unambiguously write down all generators of a given space group directly from its symbol.
@article{:/content/aip/journal/jmp/48/2/10.1063/1.2426416,
abstract = {We present a complete formulation of the two-dimensional and three-dimensional crystallographic space groups in the conformal geometric algebra of Euclidean space. This enables a simple new representation of translational and orthogonal symmetries in a multiplicative group of versors. The generators of each group are constructed directly from a basis of lattice vectors that define its crystal class. A new system of space group symbols enables one to unambiguously write down all generators of a given space group directly from its symbol.},
added-at = {2015-05-02T03:40:07.000+0200},
author = {Hestenes, David and Holt, Jeremy W.},
biburl = {https://www.bibsonomy.org/bibtex/2ce77018cf5d1c438a369dae73810396d/wolftype},
doi = {http://dx.doi.org/10.1063/1.2426416},
eid = {023514},
interhash = {f16ae7ea11fdb86184194d1c3ee74f19},
intrahash = {ce77018cf5d1c438a369dae73810396d},
journal = {Journal of Mathematical Physics},
keywords = {geometricalgebra},
number = 2,
pages = {-},
timestamp = {2015-05-02T03:40:07.000+0200},
title = {Crystallographic space groups in geometric algebra},
url = {http://scitation.aip.org/content/aip/journal/jmp/48/2/10.1063/1.2426416},
volume = 48,
year = 2007
}