Abstract
An n-dimensional crystallographic group Γ is a discrete, cocompact subgroup of the group of isometries of Euclidean n-space. Each γ ∈ Γ can be written in the form v γ + A γ , where v γ ∈ R n is a translation and A γ ∈ O(n).
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References
J. Ratcliffe, Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol. 149 (Springer, New York, 1994)
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Farley, D.S., Ortiz, I.J. (2014). The Split Three-Dimensional Crystallographic Groups. In: Algebraic K-theory of Crystallographic Groups. Lecture Notes in Mathematics, vol 2113. Springer, Cham. https://doi.org/10.1007/978-3-319-08153-3_4
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DOI: https://doi.org/10.1007/978-3-319-08153-3_4
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