Abstract
The classification of split three-dimensional crystallographic groups from Theorem 4.2 shows that seven of the groups contain all of the others as subgroups. For i = 1, …, 7, we let \(\varGamma _{i} =\langle L_{i},H_{i}\rangle\), where L i is the ith lattice (in the order that the, where L i is the ith lattice (in the order that the lattices are listed in Table 4.1) and H i is the maximal point group to be paired with L i . For instance,
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A. Hatcher, Algebraic Topology (Cambridge University Press, Cambridge, 2002)
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). Fundamental Domains for the Maximal 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_6
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DOI: https://doi.org/10.1007/978-3-319-08153-3_6
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