International Tables for Crystallography
Volume E: Subperiodic groups
First online edition (2006) ISBN: 978-1-4020-0715-6 eISBN: 978-1-4020-5410-5 doi: 10.1107/97809553602060000105
Edited by V. Kopský and D. B. Litvin
Contents
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Part 1. Subperiodic group tables: frieze-group, rod-group and layer-group types
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1.1. Symbols and terms used in Parts 1–4 (pp. 2-4) | html | pdf | chapter contents |
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References
| html | pdf |
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Tables
- Table 1.1.1. Printed symbols for crystallographic items (p. 2) | html | pdf |
- Table 1.1.2. Printed symbols for symmetry elements and for the corresponding symmetry operations (p. 2) | html | pdf |
- Table 1.1.3. Graphical symbols (pp. 3-4) | html | pdf |
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1.2. Guide to the use of the subperiodic group tables (pp. 5-28) | html | pdf | chapter contents |
- 1.2.1. Classification of subperiodic groups (pp. 5-7) | html | pdf |
- 1.2.1.1. Subperiodic group types (p. 5) | html | pdf |
- 1.2.1.2. Other classifications (pp. 5-7) | html | pdf |
- 1.2.1.2.1. Conventional coordinate systems (pp. 5-7) | html | pdf |
- 1.2.2. Contents and arrangement of the tables (p. 7) | html | pdf |
- 1.2.2.1. Subperiodic groups with more than one description (p. 7) | html | pdf |
- 1.2.3. Headline (p. 7) | html | pdf |
- 1.2.4. International (Hermann–Mauguin) symbols for subperiodic groups (pp. 7-8) | html | pdf |
- 1.2.5. Patterson symmetry (p. 8) | html | pdf |
- 1.2.6. Subperiodic group diagrams (pp. 8-12) | html | pdf |
- 1.2.7. Origin (pp. 13-14) | html | pdf |
- 1.2.8. Asymmetric unit (pp. 14-15) | html | pdf |
- 1.2.8.1. Frieze groups (p. 14) | html | pdf |
- 1.2.8.2. Rod groups (p. 14) | html | pdf |
- 1.2.8.3. Layer groups (pp. 14-15) | html | pdf |
- 1.2.9. Symmetry operations (p. 15) | html | pdf |
- 1.2.9.1. Numbering scheme (p. 15) | html | pdf |
- 1.2.9.2. Designation of symmetry operations (p. 15) | html | pdf |
- 1.2.10. Generators (pp. 15-16) | html | pdf |
- 1.2.11. Positions (p. 16) | html | pdf |
- 1.2.12. Oriented site-symmetry symbols (p. 16) | html | pdf |
- 1.2.13. Reflection conditions (p. 16) | html | pdf |
- 1.2.14. Symmetry of special projections (pp. 16-17) | html | pdf |
- 1.2.14.1. Data listed in the subperiodic group tables (pp. 16-17) | html | pdf |
- 1.2.14.2. Projections of centred subperiodic groups (p. 17) | html | pdf |
- 1.2.14.3. Projection of symmetry elements (p. 17) | html | pdf |
- 1.2.15. Maximal subgroups and minimal supergroups (pp. 17-22) | html | pdf |
- 1.2.15.1. Maximal non-isotypic non-enantiomorphic subgroups (pp. 18-20) | html | pdf |
- 1.2.15.1.1. Blocks
I
and
IIa
(pp. 19-20) | html | pdf |
- 1.2.15.1.2. Block
IIb
(p. 20) | html | pdf |
- 1.2.15.2. Maximal isotypic subgroups and enantiomorphic subgroups of lowest index (p. 20) | html | pdf |
- 1.2.15.3. Minimal non-isotypic non-enantiomorphic supergroups (pp. 20-22) | html | pdf |
- 1.2.15.4. Minimal isotypic supergroups and enantiomorphic supergroups of lowest index (p. 22) | html | pdf |
- 1.2.16. Nomenclature (p. 22) | html | pdf |
- 1.2.17. Symbols (pp. 22-27) | html | pdf |
- 1.2.17.1. Frieze groups (pp. 26-27) | html | pdf |
- 1.2.17.2. Rod groups (p. 27) | html | pdf |
- 1.2.17.3. Layer groups (p. 27) | html | pdf |
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References
| html | pdf |
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Figures
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Tables
- Table 1.2.1.1. Classification of layer groups (p. 6) | html | pdf |
- Table 1.2.1.2. Classification of rod groups (p. 6) | html | pdf |
- Table 1.2.1.3. Classification of frieze groups (p. 6) | html | pdf |
- Table 1.2.4.1. Sets of symmetry directions and their positions in the Hermann–Mauguin symbol (p. 8) | html | pdf |
- Table 1.2.5.1. Patterson symmetries for subperiodic groups (p. 8) | html | pdf |
- Table 1.2.6.1. Distinct Hermann–Mauguin symbols for monoclinic/rectangular and orthorhombic/rectangular layer groups in different settings (p. 9) | html | pdf |
- Table 1.2.6.2. Distinct Hermann–Mauguin symbols for monoclinic and orthorhombic rod groups in different settings (p. 13) | html | pdf |
- Table 1.2.6.3. Distinct Hermann–Mauguin symbols for tetragonal, trigonal and hexagonal rod groups in different settings (p. 13) | html | pdf |
- Table 1.2.6.4. Distinct Hermann–Mauguin symbols for frieze groups in different settings (p. 14) | html | pdf |
- Table 1.2.13.1. General reflection conditions due to glide planes and screw axes (p. 17) | html | pdf |
- Table 1.2.14.1.
a
′,
b
′, γ′ (
a
′) of the projected conventional coordinate system in terms of
a
,
b
,
c
, α, β, γ (
a
,
b
, γ) of the conventional coordinate system of the layer and rod groups (frieze groups) (p. 18) | html | pdf |
- Table 1.2.14.2. Projection of three-dimensional symmetry elements (layer and rod groups) (p. 19) | html | pdf |
- Table 1.2.14.3. Projection of two-dimensional symmetry elements (frieze groups) (p. 19) | html | pdf |
- Table 1.2.17.1. Frieze-group symbols (p. 20) | html | pdf |
- Table 1.2.17.2. Rod-group symbols (pp. 21-22) | html | pdf |
- Table 1.2.17.3. Layer-group symbols (pp. 23-26) | html | pdf |
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Part 2. The 7 frieze groups
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Part 3. The 75 rod groups
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3.1. The 75 rod groups (pp. 37-217) | html | | chapter contents |
- Rod group 1 (pp. 38-39) | html | pdf |
- Rod group 2 (pp. 40-41) | html | pdf |
- Rod group 3 (pp. 42-43) | html | pdf |
- Rod group 4 (pp. 44-45) | html | pdf |
- Rod group 5 (pp. 46-47) | html | pdf |
- Rod group 6 (pp. 48-49) | html | pdf |
- Rod group 7 (pp. 50-51) | html | pdf |
- Rod group 8 (pp. 52-53) | html | pdf |
- Rod group 9 (pp. 54-55) | html | pdf |
- Rod group 10 (pp. 56-57) | html | pdf |
- Rod group 11 (pp. 58-59) | html | pdf |
- Rod group 12 (pp. 60-61) | html | pdf |
- Rod group 13 (pp. 62-63) | html | pdf |
- Rod group 14 (pp. 64-65) | html | pdf |
- Rod group 15 (pp. 66-67) | html | pdf |
- Rod group 16 (pp. 68-69) | html | pdf |
- Rod group 17 (pp. 70-71) | html | pdf |
- Rod group 18 (pp. 72-73) | html | pdf |
- Rod group 19 (pp. 74-75) | html | pdf |
- Rod group 20 (pp. 76-77) | html | pdf |
- Rod group 21 (pp. 78-79) | html | pdf |
- Rod group 22 (pp. 80-81) | html | pdf |
- Rod group 23 (pp. 82-83) | html | pdf |
- Rod group 24 (pp. 84-85) | html | pdf |
- Rod group 25 (pp. 86-87) | html | pdf |
- Rod group 26 (pp. 88-89) | html | pdf |
- Rod group 27 (pp. 90-91) | html | pdf |
- Rod group 28 (pp. 92-93) | html | pdf |
- Rod group 29 (pp. 94-95) | html | pdf |
- Rod group 30 (pp. 96-97) | html | pdf |
- Rod group 31 (pp. 98-99) | html | pdf |
- Rod group 32 (pp. 100-101) | html | pdf |
- Rod group 33 (pp. 102-103) | html | pdf |
- Rod group 34 (pp. 104-105) | html | pdf |
- Rod group 35 (pp. 106-109) | html | pdf |
- Rod group 35, first setting (pp. 106-107) | html | pdf |
- Rod group 35, second setting (pp. 108-109) | html | pdf |
- Rod group 36 (pp. 110-111) | html | pdf |
- Rod group 37 (pp. 112-115) | html | pdf |
- Rod group 37, first setting (pp. 112-113) | html | pdf |
- Rod group 37, second setting (pp. 114-115) | html | pdf |
- Rod group 38 (pp. 116-119) | html | pdf |
- Rod group 38, first setting (pp. 116-117) | html | pdf |
- Rod group 38, second setting (pp. 118-119) | html | pdf |
- Rod group 39 (pp. 120-121) | html | pdf |
- Rod group 40 (pp. 122-123) | html | pdf |
- Rod group 41 (pp. 124-127) | html | pdf |
- Rod group 41, first setting (pp. 124-125) | html | pdf |
- Rod group 41, second setting (pp. 126-127) | html | pdf |
- Rod group 42 (pp. 128-129) | html | pdf |
- Rod group 43 (pp. 130-131) | html | pdf |
- Rod group 44 (pp. 132-133) | html | pdf |
- Rod group 45 (pp. 134-135) | html | pdf |
- Rod group 46 (pp. 136-139) | html | pdf |
- Rod group 46, first setting (pp. 136-137) | html | pdf |
- Rod group 46, second setting (pp. 138-139) | html | pdf |
- Rod group 47 (pp. 140-143) | html | pdf |
- Rod group 47, first setting (pp. 140-141) | html | pdf |
- Rod group 47, second setting (pp. 142-143) | html | pdf |
- Rod group 48 (pp. 144-147) | html | pdf |
- Rod group 48, first setting (pp. 144-145) | html | pdf |
- Rod group 48, second setting (pp. 146-147) | html | pdf |
- Rod group 49 (pp. 148-151) | html | pdf |
- Rod group 49, first setting (pp. 148-149) | html | pdf |
- Rod group 49, second setting (pp. 150-151) | html | pdf |
- Rod group 50 (pp. 152-155) | html | pdf |
- Rod group 50, first setting (pp. 152-153) | html | pdf |
- Rod group 50, second setting (pp. 154-155) | html | pdf |
- Rod group 51 (pp. 156-159) | html | pdf |
- Rod group 51, first setting (pp. 156-157) | html | pdf |
- Rod group 51, second setting (pp. 158-159) | html | pdf |
- Rod group 52 (pp. 160-163) | html | pdf |
- Rod group 52, first setting (pp. 160-161) | html | pdf |
- Rod group 52, second setting (pp. 162-163) | html | pdf |
- Rod group 53 (pp. 164-165) | html | pdf |
- Rod group 54 (pp. 166-167) | html | pdf |
- Rod group 55 (pp. 168-169) | html | pdf |
- Rod group 56 (pp. 170-171) | html | pdf |
- Rod group 57 (pp. 172-173) | html | pdf |
- Rod group 58 (pp. 174-175) | html | pdf |
- Rod group 59 (pp. 176-177) | html | pdf |
- Rod group 60 (pp. 178-179) | html | pdf |
- Rod group 61 (pp. 180-181) | html | pdf |
- Rod group 62 (pp. 182-183) | html | pdf |
- Rod group 63 (pp. 184-185) | html | pdf |
- Rod group 64 (pp. 186-187) | html | pdf |
- Rod group 65 (pp. 188-189) | html | pdf |
- Rod group 66 (pp. 190-191) | html | pdf |
- Rod group 67 (pp. 192-193) | html | pdf |
- Rod group 68 (pp. 194-195) | html | pdf |
- Rod group 69 (pp. 196-197) | html | pdf |
- Rod group 70 (pp. 198-201) | html | pdf |
- Rod group 70, first setting (pp. 198-199) | html | pdf |
- Rod group 70, second setting (pp. 200-201) | html | pdf |
- Rod group 71 (pp. 202-205) | html | pdf |
- Rod group 71, first setting (pp. 202-203) | html | pdf |
- Rod group 71, second setting (pp. 204-205) | html | pdf |
- Rod group 72 (pp. 206-209) | html | pdf |
- Rod group 72, first setting (pp. 206-207) | html | pdf |
- Rod group 72, second setting (pp. 208-209) | html | pdf |
- Rod group 73 (pp. 210-211) | html | pdf |
- Rod group 74 (pp. 212-213) | html | pdf |
- Rod group 75 (pp. 214-217) | html | pdf |
- Rod group 75, first setting (pp. 214-215) | html | pdf |
- Rod group 75, second setting (pp. 216-217) | html | pdf |
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Part 4. The 80 layer groups
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4.1. The 80 layer groups (pp. 219-389) | html | | chapter contents |
- Layer group 1 (pp. 220-221) | html | pdf |
- Layer group 2 (pp. 222-223) | html | pdf |
- Layer group 3 (pp. 224-225) | html | pdf |
- Layer group 4 (pp. 226-227) | html | pdf |
- Layer group 5 (pp. 228-231) | html | pdf |
- Layer group 6 (pp. 232-233) | html | pdf |
- Layer group 7 (pp. 234-237) | html | pdf |
- Layer group 8 (pp. 238-239) | html | pdf |
- Layer group 9 (pp. 240-241) | html | pdf |
- Layer group 10 (pp. 242-243) | html | pdf |
- Layer group 11 (pp. 244-245) | html | pdf |
- Layer group 12 (pp. 246-247) | html | pdf |
- Layer group 13 (pp. 248-249) | html | pdf |
- Layer group 14 (pp. 250-251) | html | pdf |
- Layer group 15 (pp. 252-253) | html | pdf |
- Layer group 16 (pp. 254-255) | html | pdf |
- Layer group 17 (pp. 256-257) | html | pdf |
- Layer group 18 (pp. 258-259) | html | pdf |
- Layer group 19 (pp. 260-261) | html | pdf |
- Layer group 20 (pp. 262-263) | html | pdf |
- Layer group 21 (pp. 264-265) | html | pdf |
- Layer group 22 (pp. 266-267) | html | pdf |
- Layer group 23 (pp. 268-269) | html | pdf |
- Layer group 24 (pp. 270-271) | html | pdf |
- Layer group 25 (pp. 272-273) | html | pdf |
- Layer group 26 (pp. 274-275) | html | pdf |
- Layer group 27 (pp. 276-277) | html | pdf |
- Layer group 28 (pp. 278-279) | html | pdf |
- Layer group 29 (pp. 280-281) | html | pdf |
- Layer group 30 (pp. 282-283) | html | pdf |
- Layer group 31 (pp. 284-285) | html | pdf |
- Layer group 32 (pp. 286-287) | html | pdf |
- Layer group 33 (pp. 288-289) | html | pdf |
- Layer group 34 (pp. 290-291) | html | pdf |
- Layer group 35 (pp. 292-293) | html | pdf |
- Layer group 36 (pp. 294-295) | html | pdf |
- Layer group 37 (pp. 296-297) | html | pdf |
- Layer group 38 (pp. 298-299) | html | pdf |
- Layer group 39 (pp. 300-301) | html | pdf |
- Layer group 40 (pp. 302-303) | html | pdf |
- Layer group 41 (pp. 304-305) | html | pdf |
- Layer group 42 (pp. 306-307) | html | pdf |
- Layer group 43 (pp. 308-309) | html | pdf |
- Layer group 44 (pp. 310-311) | html | pdf |
- Layer group 45 (pp. 312-313) | html | pdf |
- Layer group 46 (pp. 314-315) | html | pdf |
- Layer group 47 (pp. 316-317) | html | pdf |
- Layer group 48 (pp. 318-319) | html | pdf |
- Layer group 49 (pp. 320-321) | html | pdf |
- Layer group 50 (pp. 322-323) | html | pdf |
- Layer group 51 (pp. 324-325) | html | pdf |
- Layer group 52 (pp. 326-329) | html | pdf |
- Layer group 52, origin choice 1 (pp. 326-327) | html | pdf |
- Layer group 52, origin choice 2 (pp. 328-329) | html | pdf |
- Layer group 53 (pp. 330-331) | html | pdf |
- Layer group 54 (pp. 332-333) | html | pdf |
- Layer group 55 (pp. 334-335) | html | pdf |
- Layer group 56 (pp. 336-337) | html | pdf |
- Layer group 57 (pp. 338-339) | html | pdf |
- Layer group 58 (pp. 340-341) | html | pdf |
- Layer group 59 (pp. 342-343) | html | pdf |
- Layer group 60 (pp. 344-345) | html | pdf |
- Layer group 61 (pp. 346-347) | html | pdf |
- Layer group 62 (pp. 348-351) | html | pdf |
- Layer group 62, origin choice 1 (pp. 348-349) | html | pdf |
- Layer group 62, origin choice 2 (pp. 350-351) | html | pdf |
- Layer group 63 (pp. 352-353) | html | pdf |
- Layer group 64 (pp. 354-357) | html | pdf |
- Layer group 64, origin choice 1 (pp. 354-355) | html | pdf |
- Layer group 64, origin choice 2 (pp. 356-357) | html | pdf |
- Layer group 65 (pp. 358-359) | html | pdf |
- Layer group 66 (pp. 360-361) | html | pdf |
- Layer group 67 (pp. 362-363) | html | pdf |
- Layer group 68 (pp. 364-365) | html | pdf |
- Layer group 69 (pp. 366-367) | html | pdf |
- Layer group 70 (pp. 368-369) | html | pdf |
- Layer group 71 (pp. 370-371) | html | pdf |
- Layer group 72 (pp. 372-373) | html | pdf |
- Layer group 73 (pp. 374-375) | html | pdf |
- Layer group 74 (pp. 376-377) | html | pdf |
- Layer group 75 (pp. 378-379) | html | pdf |
- Layer group 76 (pp. 380-381) | html | pdf |
- Layer group 77 (pp. 382-383) | html | pdf |
- Layer group 78 (pp. 384-385) | html | pdf |
- Layer group 79 (pp. 386-387) | html | pdf |
- Layer group 80 (pp. 388-389) | html | pdf |
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Part 5. Scanning of space groups
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5.2. Guide to the use of the scanning tables (pp. 393-416) | html | pdf | chapter contents |
- 5.2.1. Introduction (pp. 393-394) | html | pdf |
- 5.2.2. The basic concepts of the scanning (pp. 394-398) | html | pdf |
- 5.2.2.1. The scanning for sectional layer groups (pp. 394-395) | html | pdf |
- 5.2.2.2. The scanning group and the scanning theorem (p. 395) | html | pdf |
- 5.2.2.3. The conventional basis of the scanning group (pp. 395-396) | html | pdf |
- 5.2.2.4. The types of scanning (p. 396) | html | pdf |
- 5.2.2.5. Orientation orbits (pp. 396-397) | html | pdf |
- 5.2.2.6. Linear orbits (pp. 397-398) | html | pdf |
- 5.2.2.7. Orthogonal, inclined and triclinic scanning (p. 398) | html | pdf |
- 5.2.3. The contents and arrangement of the scanning tables (pp. 398-402) | html | pdf |
- 5.2.3.1. The standard format (pp. 398-401) | html | pdf |
- 5.2.3.1.1. Headline (pp. 398-399) | html | pdf |
- 5.2.3.1.2. Orientation orbit (p. 399) | html | pdf |
- 5.2.3.1.3. The scanning group and its conventional basis (pp. 399-400) | html | pdf |
- 5.2.3.1.4. The linear orbits and sectional layer groups (pp. 400-401) | html | pdf |
- 5.2.3.2. Auxiliary tables (pp. 401-402) | html | pdf |
- 5.2.3.2.1. Tables of orientation orbits and auxiliary bases of scanning groups (p. 401) | html | pdf |
- 5.2.3.2.2. Reference tables (pp. 401-402) | html | pdf |
- 5.2.4. Guidelines for individual systems (pp. 402-410) | html | pdf |
- 5.2.4.1. Triclinic system (p. 402) | html | pdf |
- 5.2.4.2. Monoclinic system (pp. 402-403) | html | pdf |
- 5.2.4.3. Orthorhombic system (pp. 403-404) | html | pdf |
- 5.2.4.3.1. Orthogonal scanning, standard tables (p. 403) | html | pdf |
- 5.2.4.3.2. Inclined scanning, auxiliary tables (pp. 403-404) | html | pdf |
- 5.2.4.4. Tetragonal system (pp. 404-405) | html | pdf |
- 5.2.4.4.1. Orthogonal scanning, standard tables (p. 404) | html | pdf |
- 5.2.4.4.2. Inclined scanning, auxiliary tables (pp. 404-405) | html | pdf |