Crystallographic space groups in geometric algebra Academic Article

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. © 2007 American Institute of Physics.

authors

• Holt, Jeremy

author list (cited authors)

• Hestenes, D., & Holt, J. W

complete list of authors

• Hestenes, David||Holt, Jeremy W

publication date

• January 1, 2007 11:11 AM

publisher

• AIP Publishing  Publisher

published in

• Journal of Mathematical Physics  Journal

Digital Object Identifier (DOI)

• 10.1063/1.2426416

start page

• 023514

end page

• 023514

volume

• 48

issue

• 2