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Space group determination

22 bytes removed, 13:18, 9 July 2020
Subgroup and supergroup relations of these space groups
=== Subgroup and supergroup relations of these space groups ===Compiled from [ International Tables for Crystallography (2006) Vol. A1 (Wiley)]. Simply put, for each space group, a maximum ''translationengleiche'' subgroup has lost a single type of symmetry, and a minimum ''translationengleiche'' supergroup has gained a single symmetry type. Example: P222 is a supergroup of P2, and a subgroup of P422 (and P4222 and P23). Of course the subgroupsub-/supergroup relation is recursive, which is why P1 is also a (sub-)subgroup of P222 (but not a maximum ''translationengleiche'' subgroup). The table below does not show other types of sub/supergroup relations, e.g. non-isomorphic ''klassengleiche'' supergroups which may result e.g. from centring translations, because I find them less relevant in space group determination. The table below is relevant because in particular twinning adds a symmetry type, and leads to an apparent space group which is the supergroup of the true space group.
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! spacegroup

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