Results for DC.creator="A." AND DC.creator="Looijenga-Vos" in section 9.8.4 of volume C   page 1 of 2 pages.
Theoretical foundation
International Tables for Crystallography (2006). Vol. C, Section 9.8.4, pp. 937-945
Theoretical foundation 9.8.4. Theoretical foundation 9.8.4.1. Lattices and metric | | A periodic crystal structure is defined in a three-dimensional Euclidean space V and is invariant with respect ... three fundamental ones : These translations are linearly independent and span a lattice [Lambda]. The dimension of [Lambda] is the ...

Equivalent positions and modulation relations
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.2, pp. 940-941
... positions and modulation relations 9.8.4.4.2. Equivalent positions and modulation relations A (3 + d)-dimensional space group that leaves a function invariant maps points in (3 + d)-space to points ... the function has the same value. The atomic positions of a modulated crystal represent such a pattern, and the superspace ...

Symmetry elements
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.1, p. 940
Symmetry elements 9.8.4.4.1. Symmetry elements The elements of a (3 + d)-dimensional superspace group are pairs of Euclidean transformations ... direct product of the corresponding Euclidean groups. The elements form a three-dimensional space group, but the same does not hold ... translation v in V [see (9.8.4.32)]. In other words, a basis of the lattice does not simply split into ...

Superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4, pp. 940-941
... groups 9.8.4.4. Superspace groups 9.8.4.4.1. Symmetry elements | | The elements of a (3 + d)-dimensional superspace group are pairs of Euclidean transformations ... direct product of the corresponding Euclidean groups. The elements form a three-dimensional space group, but the same does not hold ... translation v in V [see (9.8.4.32)]. In other words, a basis of the lattice does not simply split into ...

Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.3, p. 940
... are arithmetically equivalent. This means that each of them admits a lattice basis of standard form such that their holohedral point ...

Crystallographic systems
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.2, p. 940
Crystallographic systems 9.8.4.3.2. Crystallographic systems Definition 5.A crystallographic system is a set of lattices having geometrically equivalent holohedral point groups. In this way, a given holohedral point group (and even each crystallographic point group ...

Holohedry
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.1, pp. 939-940
... 9.8.4.3.1. Holohedry The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed ... vector module M* is the projection. Conversely, if one has a point group that leaves the (3 + d)-dimensional lattice ...

Systems and Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3, pp. 939-940
... 9.8.4.3.1. Holohedry | | The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed ... vector module M* is the projection. Conversely, if one has a point group that leaves the (3 + d)-dimensional lattice ...

Geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.2, p. 939
... to the previous section, in the case of modulated structures a standard basis can be chosen (for M* and correspondingly for ... operation R that leaves the diffraction pattern invariant, there is a point-group transformation in the external space (the physical one, so that ) and a point-group transformation in the internal space, such that ...

Laue class
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.1, pp. 938-939
... group in three dimensions that transforms every diffraction peak into a peak of the same intensity.2 Because all diffraction vectors are ... is given by The (3 + d) × (3 + d) matrices form a finite group of integral matrices for K equal to or to one of its subgroups. A well known theorem in algebra states that then there ...

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