%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 }