Abstract
Let L be a lattice in \(\mathbb{R}^{3}\), and let H ≤ O(3) be a point group such that H ⋅ L = L. In this chapter, we classify pairs (L, H) up to arithmetic equivalence (defined below). The equivalence classes of pairs (L, H) are in one-to-one correspondence with isomorphism classes of split crystallographic groups (see Chap. 4).
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References
R.L.E. Schwarzenberger, N-Dimensional Crystallography. Research Notes in Mathematics, vol. 41 (Pittman Advanced Publishing Program, Boston, Mass.-London 1980)
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Farley, D.S., Ortiz, I.J. (2014). Arithmetic Classification of Pairs (L, H). 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_3
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DOI: https://doi.org/10.1007/978-3-319-08153-3_3
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