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Results for DC.creator="Y." AND DC.creator="Billiet" in section 2.1.5 of volume A1 |
Series of maximal isomorphic subgroups
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5, pp. 82-84 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Trigonal space groups with rhombohedral lattice
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.2, p. 83 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Monoclinic space groups
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.1, p. 83 [ doi:10.1107/97809553602060000797 ]
Monoclinic space groups 2.1.5.5.1. Monoclinic space groups In the monoclinic space groups, the series in the listings `unique axis b' and `unique axis c' are closely related by a simple cyclic permutation of the axes a, b and c, see IT A, Section 2.2.16 . References International Tables for Crystallography (2011 ...
Special series
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5, pp. 83-84 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Generators
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.4, pp. 82-83 [ doi:10.1107/97809553602060000797 ]
Generators 2.1.5.4. Generators The generators of the p (or or ) conjugate isomorphic subgroups are obtained from those of by adding translational components. These components are determined by the parameters p (or q and r, if relevant) and u (and v and w, if relevant). Example 2.1.5.4.1 Space group , No. 198. ...
Origin shift
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.3, p. 82 [ doi:10.1107/97809553602060000797 ]
Origin shift 2.1.5.3. Origin shift Each of the sublattices discussed in Section 2.1.4.3.2 is common to a conjugacy class or belongs to a normal subgroup of a given series. The subgroups in a conjugacy class differ by the positions of their conventional origins relative to the origin of the space group ...
Basis transformation
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.2, p. 82 [ doi:10.1107/97809553602060000797 ]
Basis transformation 2.1.5.2. Basis transformation The conventional basis of the unit cell of each isomorphic subgroup in the series has to be defined relative to the basis of the original space group. For this definition the prime p is frequently sufficient as a parameter. Example 2.1.5.2.1 The isomorphic subgroups of the ...
General description
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.1, p. 82 [ doi:10.1107/97809553602060000797 ]
General description 2.1.5.1. General description Maximal subgroups of index higher than 4 have index p, or , where p is prime, are necessarily isomorphic subgroups and are infinite in number. Only a few of them are listed in IT A in the block `Maximal isomorphic subgroups of lowest index IIc'. Because ...
Space groups with two origin choices
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.3, pp. 83-84 [ doi:10.1107/97809553602060000797 ]
Space groups with two origin choices 2.1.5.5.3. Space groups with two origin choices Space groups with two origin choices are always described in the same basis, but origin 1 is shifted relative to origin 2 by the shift vector s. For most space groups with two origins, the appearance of the ...
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5, pp. 82-84 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Trigonal space groups with rhombohedral lattice
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.2, p. 83 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Monoclinic space groups
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.1, p. 83 [ doi:10.1107/97809553602060000797 ]
Monoclinic space groups 2.1.5.5.1. Monoclinic space groups In the monoclinic space groups, the series in the listings `unique axis b' and `unique axis c' are closely related by a simple cyclic permutation of the axes a, b and c, see IT A, Section 2.2.16 . References International Tables for Crystallography (2011 ...
Special series
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5, pp. 83-84 [ doi:10.1107/97809553602060000797 ]
... rhombohedral axes, equation (2.1.5.1) would be written with the matrix Y to be determined. The transformation from hexagonal to rhombohedral axes ... one gets From equation (2.1.5.4) it follows that One obtains Y from equation (2.1.5.5) by matrix multiplication, and from Y for the bases of the subgroups with rhombohedral axesThe ...
Generators
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.4, pp. 82-83 [ doi:10.1107/97809553602060000797 ]
Generators 2.1.5.4. Generators The generators of the p (or or ) conjugate isomorphic subgroups are obtained from those of by adding translational components. These components are determined by the parameters p (or q and r, if relevant) and u (and v and w, if relevant). Example 2.1.5.4.1 Space group , No. 198. ...
Origin shift
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.3, p. 82 [ doi:10.1107/97809553602060000797 ]
Origin shift 2.1.5.3. Origin shift Each of the sublattices discussed in Section 2.1.4.3.2 is common to a conjugacy class or belongs to a normal subgroup of a given series. The subgroups in a conjugacy class differ by the positions of their conventional origins relative to the origin of the space group ...
Basis transformation
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.2, p. 82 [ doi:10.1107/97809553602060000797 ]
Basis transformation 2.1.5.2. Basis transformation The conventional basis of the unit cell of each isomorphic subgroup in the series has to be defined relative to the basis of the original space group. For this definition the prime p is frequently sufficient as a parameter. Example 2.1.5.2.1 The isomorphic subgroups of the ...
General description
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.1, p. 82 [ doi:10.1107/97809553602060000797 ]
General description 2.1.5.1. General description Maximal subgroups of index higher than 4 have index p, or , where p is prime, are necessarily isomorphic subgroups and are infinite in number. Only a few of them are listed in IT A in the block `Maximal isomorphic subgroups of lowest index IIc'. Because ...
Space groups with two origin choices
International Tables for Crystallography (2011). Vol. A1, Section 2.1.5.5.3, pp. 83-84 [ doi:10.1107/97809553602060000797 ]
Space groups with two origin choices 2.1.5.5.3. Space groups with two origin choices Space groups with two origin choices are always described in the same basis, but origin 1 is shifted relative to origin 2 by the shift vector s. For most space groups with two origins, the appearance of the ...
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