International Tables for Crystallography
Volume A: Space-group symmetry

First online edition (2006)   ISBN: 978-0-7923-6590-7   eISBN: 978-1-4020-5406-8   doi: 10.1107/97809553602060000100

Edited by Th. Hahn

Contents

• Foreword to the Fifth, Revised Edition  (p. xv) | html | pdf |
  Th. Hahn
  Preface  (pp. xvi-xvii) | html | pdf |
  Th. Hahn
  Computer Production of Volume A  (pp. xix-xx) | html | pdf |
  M. I. Aroyo and P. B. Konstantinov

• Part 1. Symbols and terms used in this volume
  • 1.1. Printed symbols for crystallographic items  (pp. 2-3) | html | pdf | chapter contents |
    Th. Hahn
    • 1.1.1. Vectors, coefficients and coordinates  (p. 2) | html | pdf |
    • 1.1.2. Directions and planes  (p. 2) | html | pdf |
    • 1.1.3. Reciprocal space  (p. 2) | html | pdf |
    • 1.1.4. Functions  (p. 2) | html | pdf |
    • 1.1.5. Spaces  (p. 3) | html | pdf |
    • 1.1.6. Motions and matrices  (p. 3) | html | pdf |
    • 1.1.7. Groups  (p. 3) | html | pdf |
  • 1.2. Printed symbols for conventional centring types  (p. 4) | html | pdf | chapter contents |
    Th. Hahn
    • 1.2.1. Printed symbols for the conventional centring types of one-, two- and three-dimensional cells  (p. 4) | html | pdf |
    • 1.2.2. Notes on centred cells  (p. 4) | html | pdf |
    • References | html | pdf |
  • 1.3. Printed symbols for symmetry elements  (pp. 5-6) | html | pdf | chapter contents |
    Th. Hahn
    • 1.3.1. Printed symbols for symmetry elements and for the corresponding symmetry operations in one, two and three dimensions  (p. 5) | html | pdf |
    • 1.3.2. Notes on symmetry elements and symmetry operations  (p. 6) | html | pdf |
    • References | html | pdf |
  • 1.4. Graphical symbols for symmetry elements in one, two and three dimensions  (pp. 7-11) | html | pdf | chapter contents |
    Th. Hahn
    • 1.4.1. Symmetry planes normal to the plane of projection (three dimensions) and symmetry lines in the plane of the figure (two dimensions)  (p. 7) | html | pdf |
    • 1.4.2. Symmetry planes parallel to the plane of projection  (p. 7) | html | pdf |
    • 1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes and only)  (p. 8) | html | pdf |
    • 1.4.4. Notes on graphical symbols of symmetry planes  (p. 8) | html | pdf |
    • 1.4.5. Symmetry axes normal to the plane of projection and symmetry points in the plane of the figure  (p. 9) | html | pdf |
    • 1.4.6. Symmetry axes parallel to the plane of projection  (p. 10) | html | pdf |
    • 1.4.7. Symmetry axes inclined to the plane of projection (in cubic space groups only)  (p. 10) | html | pdf |
    • References | html | pdf |

• Part 2. Guide to the use of the space-group tables
  • 2.1. Classification and coordinate systems of space groups  (pp. 14-16) | html | pdf | chapter contents |
    Th. Hahn and A. Looijenga-Vos
    • 2.1.1. Introduction  (p. 14) | html | pdf |
    • 2.1.2. Space-group classification  (p. 14) | html | pdf |
    • 2.1.3. Conventional coordinate systems and cells  (pp. 14-16) | html | pdf |
    • References | html | pdf |
  • 2.2. Contents and arrangement of the tables  (pp. 17-41) | html | pdf | chapter contents |
    Th. Hahn and A. Looijenga-Vos
    • 2.2.1. General layout  (p. 17) | html | pdf |
    • 2.2.2. Space groups with more than one description  (p. 17) | html | pdf |
    • 2.2.3. Headline  (pp. 17-18) | html | pdf |
    • 2.2.4. International (Hermann–Mauguin) symbols for plane groups and space groups ( cf. Chapter 12.2 )  (pp. 18-19) | html | pdf |
    • 2.2.5. Patterson symmetry  (p. 19) | html | pdf |
    • 2.2.6. Space-group diagrams  (pp. 20-24) | html | pdf |
    • 2.2.7. Origin  (pp. 24-25) | html | pdf |
    • 2.2.8. Asymmetric unit  (pp. 25-26) | html | pdf |
    • 2.2.9. Symmetry operations  (pp. 26-27) | html | pdf |
    • 2.2.10. Generators  (p. 27) | html | pdf |
    • 2.2.11. Positions  (pp. 27-28) | html | pdf |
    • 2.2.12. Oriented site-symmetry symbols  (pp. 28-29) | html | pdf |
    • 2.2.13. Reflection conditions  (pp. 29-32) | html | pdf |
    • 2.2.14. Symmetry of special projections  (pp. 33-35) | html | pdf |
    • 2.2.15. Maximal subgroups and minimal supergroups  (pp. 35-38) | html | pdf |
    • 2.2.16. Monoclinic space groups  (pp. 38-40) | html | pdf |
    • 2.2.17. Crystallographic groups in one dimension  (p. 40) | html | pdf |
    • References | html | pdf |

• Part 3. Determination of space groups
  • 3.1. Space-group determination and diffraction symbols  (pp. 44-54) | html | pdf | chapter contents |
    A. Looijenga-Vos and M. J. Buerger
    • 3.1.1. Introduction  (p. 44) | html | pdf |
    • 3.1.2. Laue class and cell  (p. 44) | html | pdf |
    • 3.1.3. Reflection conditions and diffraction symbol  (pp. 44-45) | html | pdf |
    • 3.1.4. Deduction of possible space groups  (pp. 45-46) | html | pdf |
    • 3.1.5. Diffraction symbols and possible space groups  (pp. 46-51) | html | pdf |
    • 3.1.6. Space-group determination by additional methods  (pp. 51-53) | html | pdf |
    • References | html | pdf |

• Part 4. Synoptic tables of space-group symbols
  • 4.1. Introduction to the synoptic tables  (pp. 56-60) | html | pdf | chapter contents |
    E. F. Bertaut
    • 4.1.1. Introduction  (p. 56) | html | pdf |
    • 4.1.2. Additional symmetry elements  (pp. 56-60) | html | pdf |
    • References | html | pdf |
  • 4.2. Symbols for plane groups (two-dimensional space groups)  (p. 61) | html | pdf | chapter contents |
    E. F. Bertaut
    • 4.2.1. Arrangement of the tables  (p. 61) | html | pdf |
    • 4.2.2. Additional symmetry elements and extended symbols  (p. 61) | html | pdf |
    • 4.2.3. Multiple cells  (p. 61) | html | pdf |
    • 4.2.4. Group–subgroup relations  (p. 61) | html | pdf |
    • References | html | pdf |
  • 4.3. Symbols for space groups  (pp. 62-76) | html | pdf | chapter contents |
    E. F. Bertaut
    • 4.3.1. Triclinic system  (p. 62) | html | pdf |
    • 4.3.2. Monoclinic system  (pp. 62-68) | html | pdf |
    • 4.3.3. Orthorhombic system  (pp. 68-71) | html | pdf |
    • 4.3.4. Tetragonal system  (pp. 71-73) | html | pdf |
    • 4.3.5. Trigonal and hexagonal systems  (pp. 73-75) | html | pdf |
    • 4.3.6. Cubic system  (pp. 75-76) | html | pdf |
    • References | html | pdf |

• Part 5. Transformations in crystallography
  • 5.1. Transformations of the coordinate system (unit-cell transformations)  (pp. 78-85) | html | pdf | chapter contents |
    H. Arnold
    • 5.1.1. Introduction  (p. 78) | html | pdf |
    • 5.1.2. Matrix notation  (p. 78) | html | pdf |
    • 5.1.3. General transformation  (pp. 78-85) | html | pdf |
  • 5.2. Transformations of symmetry operations (motions)  (pp. 86-89) | html | pdf | chapter contents |
    H. Arnold
    • 5.2.1. Transformations  (p. 86) | html | pdf |
    • 5.2.2. Invariants  (pp. 86-87) | html | pdf |
    • 5.2.3. Example: low cristobalite and high cristobalite  (pp. 87-89) | html | pdf |
    • References | html | pdf |

• Part 6. The 17 plane groups (two-dimensional space groups)
  • 6.1. The 17 plane groups (two-dimensional space groups)  (pp. 92-109) | html | | chapter contents |
    • Plane group 1  (p. 92) | html | pdf |
    • Plane group 2  (p. 93) | html | pdf |
    • Plane group 3  (p. 94) | html | pdf |
    • Plane group 4  (p. 95) | html | pdf |
    • Plane group 5  (p. 96) | html | pdf |
    • Plane group 6  (p. 97) | html | pdf |
    • Plane group 7  (p. 98) | html | pdf |
    • Plane group 8  (p. 99) | html | pdf |
    • Plane group 9  (p. 100) | html | pdf |
    • Plane group 10  (p. 101) | html | pdf |
    • Plane group 11  (p. 102) | html | pdf |
    • Plane group 12  (p. 103) | html | pdf |
    • Plane group 13  (p. 104) | html | pdf |
    • Plane group 14  (p. 105) | html | pdf |
    • Plane group 15  (p. 106) | html | pdf |
    • Plane group 16  (p. 107) | html | pdf |
    • Plane group 17  (pp. 108-109) | html | pdf |

• Part 7. The 230 space groups
  • 7.1. The 230 space groups  (pp. 112-717) | html | | chapter contents |
    • Space group 1  (pp. 112-113) | html | pdf |
    • Space group 2  (pp. 114-115) | html | pdf |
    • Space group 3  (pp. 116-119) | html | pdf |
    • Space group 4  (pp. 120-123) | html | pdf |
    • Space group 5  (pp. 124-131) | html | pdf |
    • Space group 6  (pp. 132-135) | html | pdf |
    • Space group 7  (pp. 136-143) | html | pdf |
    • Space group 8  (pp. 144-151) | html | pdf |
    • Space group 9  (pp. 152-159) | html | pdf |
    • Space group 10  (pp. 160-163) | html | pdf |
    • Space group 11  (pp. 164-167) | html | pdf |
    • Space group 12  (pp. 168-175) | html | pdf |
    • Space group 13  (pp. 176-183) | html | pdf |
    • Space group 14  (pp. 184-191) | html | pdf |
    • Space group 15  (pp. 192-199) | html | pdf |
    • Space group 16  (pp. 200-201) | html | pdf |
    • Space group 17  (pp. 202-203) | html | pdf |
    • Space group 18  (pp. 204-205) | html | pdf |
    • Space group 19  (pp. 206-207) | html | pdf |
    • Space group 20  (pp. 208-209) | html | pdf |
    • Space group 21  (pp. 210-211) | html | pdf |
    • Space group 22  (pp. 212-213) | html | pdf |
    • Space group 23  (pp. 214-215) | html | pdf |
    • Space group 24  (pp. 216-217) | html | pdf |
    • Space group 25  (pp. 218-219) | html | pdf |
    • Space group 26  (pp. 220-221) | html | pdf |
    • Space group 27  (pp. 222-223) | html | pdf |
    • Space group 28  (pp. 224-225) | html | pdf |
    • Space group 29  (pp. 226-227) | html | pdf |
    • Space group 30  (pp. 228-229) | html | pdf |
    • Space group 31  (pp. 230-231) | html | pdf |
    • Space group 32  (pp. 232-233) | html | pdf |
    • Space group 33  (pp. 234-235) | html | pdf |
    • Space group 34  (pp. 236-237) | html | pdf |
    • Space group 35  (pp. 238-239) | html | pdf |
    • Space group 36  (pp. 240-241) | html | pdf |
    • Space group 37  (pp. 242-243) | html | pdf |
    • Space group 38  (pp. 244-245) | html | pdf |
    • Space group 39  (pp. 246-247) | html | pdf |
    • Space group 40  (pp. 248-249) | html | pdf |
    • Space group 41  (pp. 250-251) | html | pdf |
    • Space group 42  (pp. 252-253) | html | pdf |
    • Space group 43  (pp. 254-255) | html | pdf |
    • Space group 44  (pp. 256-257) | html | pdf |
    • Space group 45  (pp. 258-259) | html | pdf |
    • Space group 46  (pp. 260-261) | html | pdf |
    • Space group 47  (pp. 262-263) | html | pdf |
    • Space group 48  (pp. 264-267) | html | pdf |
    • Space group 49  (pp. 268-269) | html | pdf |
    • Space group 50  (pp. 270-273) | html | pdf |
    • Space group 51  (pp. 274-275) | html | pdf |
    • Space group 52  (pp. 276-277) | html | pdf |
    • Space group 53  (pp. 278-279) | html | pdf |
    • Space group 54  (pp. 280-281) | html | pdf |
    • Space group 55  (pp. 282-283) | html | pdf |
    • Space group 56  (pp. 284-285) | html | pdf |
    • Space group 57  (pp. 286-287) | html | pdf |
    • Space group 58  (pp. 288-289) | html | pdf |
    • Space group 59  (pp. 290-293) | html | pdf |
    • Space group 60  (pp. 294-295) | html | pdf |
    • Space group 61  (pp. 296-297) | html | pdf |
    • Space group 62  (pp. 298-299) | html | pdf |
    • Space group 63  (pp. 300-301) | html | pdf |
    • Space group 64  (pp. 302-303) | html | pdf |
    • Space group 65  (pp. 304-306) | html | pdf |
    • Space group 66  (pp. 308-309) | html | pdf |
    • Space group 67  (pp. 310-311) | html | pdf |
    • Space group 68  (pp. 312-315) | html | pdf |
    • Space group 69  (pp. 316-318) | html | pdf |
    • Space group 70  (pp. 320-323) | html | pdf |
    • Space group 71  (pp. 324-325) | html | pdf |
    • Space group 72  (pp. 326-327) | html | pdf |
    • Space group 73  (pp. 328-329) | html | pdf |
    • Space group 74  (pp. 330-331) | html | pdf |
    • Space group 75  (p. 332) | html | pdf |
    • Space group 76  (p. 333) | html | pdf |
    • Space group 77  (p. 334) | html | pdf |
    • Space group 78  (p. 335) | html | pdf |
    • Space group 79  (pp. 336-337) | html | pdf |
    • Space group 80  (pp. 338-339) | html | pdf |
    • Space group 81  (pp. 340-341) | html | pdf |
    • Space group 82  (pp. 342-343) | html | pdf |
    • Space group 83  (pp. 344-345) | html | pdf |
    • Space group 84  (pp. 346-347) | html | pdf |
    • Space group 85  (pp. 348-351) | html | pdf |
    • Space group 86  (pp. 352-355) | html | pdf |
    • Space group 87  (pp. 356-357) | html | pdf |
    • Space group 88  (pp. 358-361) | html | pdf |
    • Space group 89  (pp. 362-363) | html | pdf |
    • Space group 90  (pp. 364-365) | html | pdf |
    • Space group 91  (pp. 366-367) | html | pdf |
    • Space group 92  (pp. 368-369) | html | pdf |
    • Space group 93  (pp. 370-371) | html | pdf |
    • Space group 94  (pp. 372-373) | html | pdf |
    • Space group 95  (pp. 374-375) | html | pdf |
    • Space group 96  (pp. 376-377) | html | pdf |
    • Space group 97  (pp. 378-379) | html | pdf |
    • Space group 98  (pp. 380-381) | html | pdf |
    • Space group 99  (pp. 382-383) | html | pdf |
    • Space group 100  (pp. 384-385) | html | pdf |
    • Space group 101  (pp. 386-387) | html | pdf |
    • Space group 102  (pp. 388-389) | html | pdf |
    • Space group 103  (pp. 390-391) | html | pdf |
    • Space group 104  (pp. 392-393) | html | pdf |
    • Space group 105  (pp. 394-395) | html | pdf |
    • Space group 106  (pp. 396-397) | html | pdf |
    • Space group 107  (pp. 398-399) | html | pdf |
    • Space group 108  (pp. 400-401) | html | pdf |
    • Space group 109  (pp. 402-403) | html | pdf |
    • Space group 110  (pp. 404-405) | html | pdf |
    • Space group 111  (pp. 406-407) | html | pdf |
    • Space group 112  (pp. 408-409) | html | pdf |
    • Space group 113  (pp. 410-411) | html | pdf |
    • Space group 114  (pp. 412-413) | html | pdf |
    • Space group 115  (pp. 414-415) | html | pdf |
    • Space group 116  (pp. 416-417) | html | pdf |
    • Space group 117  (pp. 418-419) | html | pdf |
    • Space group 118  (pp. 420-421) | html | pdf |
    • Space group 119  (pp. 422-423) | html | pdf |
    • Space group 120  (pp. 424-425) | html | pdf |
    • Space group 121  (pp. 426-427) | html | pdf |
    • Space group 122  (pp. 428-429) | html | pdf |
    • Space group 123  (pp. 430-431) | html | pdf |
    • Space group 124  (pp. 432-433) | html | pdf |
    • Space group 125  (pp. 434-437) | html | pdf |
    • Space group 126  (pp. 438-441) | html | pdf |
    • Space group 127  (pp. 442-443) | html | pdf |
    • Space group 128  (pp. 444-445) | html | pdf |
    • Space group 129  (pp. 446-449) | html | pdf |
    • Space group 130  (pp. 450-453) | html | pdf |
    • Space group 131  (pp. 454-455) | html | pdf |
    • Space group 132  (pp. 456-457) | html | pdf |
    • Space group 133  (pp. 458-461) | html | pdf |
    • Space group 134  (pp. 462-465) | html | pdf |
    • Space group 135  (pp. 466-467) | html | pdf |
    • Space group 136  (pp. 468-469) | html | pdf |
    • Space group 137  (pp. 470-473) | html | pdf |
    • Space group 138  (pp. 474-477) | html | pdf |
    • Space group 139  (pp. 478-479) | html | pdf |
    • Space group 140  (pp. 480-481) | html | pdf |
    • Space group 141  (pp. 482-485) | html | pdf |
    • Space group 142  (pp. 486-489) | html | pdf |
    • Space group 143  (pp. 490-491) | html | pdf |