Colored symmetry: a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Pergamon Press
1964
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 263 S. Ill., graph. Darst. |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV005686107 | ||
| 003 | DE-604 | ||
| 005 | 20030213 | ||
| 007 | t | ||
| 008 | 921028s1964 ad|| |||| 00||| eng d | ||
| 035 | |a (OCoLC)612726365 | ||
| 035 | |a (DE-599)BVBBV005686107 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-355 |a DE-19 |a DE-188 | ||
| 084 | |a UQ 1300 |0 (DE-625)146478: |2 rvk | ||
| 084 | |a VE 5700 |0 (DE-625)147119:253 |2 rvk | ||
| 100 | 1 | |a Šubnikov, Aleksej V. |d 1887-1970 |e Verfasser |0 (DE-588)117462055 |4 aut | |
| 240 | 1 | 0 | |a Simmetrija i antisimmetrija konečnych figur |
| 245 | 1 | 0 | |a Colored symmetry |b a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 |c by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser |
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1964 | |
| 300 | |a XXV, 263 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Kristallsymmetrie |0 (DE-588)4136175-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kristallsymmetrie |0 (DE-588)4136175-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Belov, Nikolaj V. |d 1891-1982 |e Verfasser |0 (DE-588)134216539 |4 aut | |
| 700 | 1 | |a Holser, William T. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003551535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003551535 | ||
Record in the Search Index
| _version_ | 1804119874559016960 |
|---|---|
| adam_text | Contents
PAGE
Editor s Preface xi
Author s Preface to Part I xv
PART I
SYMMETRY AND ANTISYMMETRY OF FINITE FIGURES
a. v. shubnikov
The Symmetry of Finite Figures 3
Introduction 3
Basic Concepts and Definitions of Symmetry 3
General definition of symmetry 3
The figure 4
The uniform distribution of equal domains of a figure 4
Reflection in a plane 5
Rotations around an axis 6
Mirror rotations (rotary reflections) 7
Singular points, lines and planes. Transformations of space 8
Particles and media, in view of the broadened concept of figures 9
Equivalent and non equivalent operations 11
Inversion 11
Reflection in a straight line, or reversal 13
Identification 13
Comparison of the operations of identification, reflection, reversal
and inversion 14
The reduction of all symmetrical transformations to reflections in
planes 15
Consecutive reflection in three or more planes intersecting at one
point 1G
Consecutive reflection in three arbitrarily selected planes, intersect¬
ing at one point 17
Euler s theorem 19
Congruent and mirror equality 20
Symmetrical transformations of the first and second kind 22
Reflection as a fundamental operation of symmetry 23
On the equality of objects in general 24
v
VI CONTENTS
PAGE
Repetition of operations and powers of operations 25
The designation of operations by components of a figure 26
The product of operations 27
Symmetry Groups 27
General concept of a symmetry group 27
The order of a group 28
The asymmetric figure 28
Fundamental properties of symmetry groups 29
Point groups 31
Point groups determined by rotation through an n th part of a
revolution 31
Groups determined by rotation through any given rational part of
a full revolution 35
Groups determined by rotation through an irrational part of a
complete revolution 37
Groups determined by one mirror rotation through an angle
equal to an even part 1 / (2«) of a complete revolution 38
Groups determined by one mirror rotation through an angle equal
an odd numbered part l/(2n + 1) of a revolution 40
Groups determined by one arbitrary mirror rotation 43
Concluding remarks on the derivation of symmetry groups deter¬
mined by one operation 43
Sub groups 44
Elements of symmetry and their designation 45
Arrangement of a plane of symmetry relative to axes of symmetry 45
Groups determined by one rotation and reflection in a transverse
plane 46
Groups determined by one rotation and reflection in a longitudinal
plane 47
Groups determined by two rotations 50
On the impossibility of groups existing which require more than
two axes for their determination 61
Groups determined by two rotations and reflection 62
Concluding observations on the derivation of point groups 71
Types of symmetry groups 74
Limiting groups 75
Crystallographic groups 76
The Symmetry of Plane Figures 76
Neutral and polar plane figures 76
Plane figures of mixed polarity 77
CONTENTS vii
PAGE
Operations of symmetry of plane figures 77
Symmetry groups of finite plane figures 84
Symmetry groups of finite polar plane figures 86
Antisymmetry of Finite Figures 88
Basic Concepts and Definitions of Antisymmetry 88
The representation of symmetrical operations of three dimensional
figures by matrices of cosines 88
Symmetrical operations of three dimensional figures as afine
orthogonal transformations 92
Symmetrical operations of plane figures in two dimensional and
three dimensional space 93
Operations of antisymmetry in three dimensional figures 96
Reverse equality or anti equality of figures 97
Polar and neutral figures 98
The asymmetrical figure 99
Operation of the change of sign of a figure 100
Operations of antireflection in a plane 104
The operation of 180° antirotation 106
The operation of anti inversion 107
The general case of antirotation 108
The general case of mirror antirotation 109
Groups of Antisymmetry of Finite Figures 112
Three types of groups of antisymmetry 112
Groups of mixed polarity 114
Groups of mixed polarity determined by one operation 115
Groups of mixed polarity determined by two mutually parallel or
perpendicular elements of symmetry 119
Groups of mixed polarity determined by one axis and two planes—
longitudinal and transverse 126
Groups of mixed polarity, derived from series XIII and XIV 132
Groups of mixed polarity, derived from series XV and XVI 136
Limiting groups of mixed polarity 141
Survey of point groups of mixed polarity 141
Simple forms of groups of mixed polarity 144
Appendix
The Division of Symmetrical Figures into Equal Domains 148
Viii CONTENTS
PAGE
Examples of Antisymmetrical Figures from the Field of Physical
C rystallography 150
The Symmetry of Vectors and Tensors 153
Antisymmetry of Textures (Limiting Groups) 161
On the Terms: Dissymmetry, Asymmetry, and Antisymmetry 171
PART II
INFINITE GROUPS OF COLORED SYMMETRY
N. V. BELOV AND OTHERS
The 1651 Shubnikov Groups [Dichromatic Space Groups]—N. V.
Belov, N. N. Neronova and T. S. Smirnova 175
Introduction 175
Bravais Lattices for Shubnikov Groups 176
Symbolism. General Theorems 185
The Derivation of Shubnikov Groups 188
Dichromatic Plane Groups—N. V. Belov and T. N. Tarkhova 211
Introduction 211
Derivation of the Groups 211
An alternate derivation 218
Mosaics for the Dichromatic Plane Groups—N. V. Belov and
E. N. Belova 220
On One dimensional Infinite Crystallographic Groups—N. V.
Belov 222
Introduction 22
Line Groups in a Plane 222
Two sided or Dichromatic Line Groups in a Plane 223
Rod Groups 226
Polychromatic Plane Groups—N. V. Belov, E. N. Belova and
T. N. Tarkhova 228
Derivation 228
Mosaics for Crystallographic Groups 228
Non crystallographic Mosaics 234
CONTENTS IX
PAGF.
Three dimensional Mosaics with Colored Symmetry—N. V. Belov 238
Introduction 238
Cubic Mosaics 238
Pseudo cubic Mosaics 239
Mosaics with Polychromatic Translation 243
Literature on Symmetry 249
Supplementary References 253
Index 261
|
| any_adam_object | 1 |
| author | Šubnikov, Aleksej V. 1887-1970 Belov, Nikolaj V. 1891-1982 |
| author_GND | (DE-588)117462055 (DE-588)134216539 |
| author_facet | Šubnikov, Aleksej V. 1887-1970 Belov, Nikolaj V. 1891-1982 |
| author_role | aut aut |
| author_sort | Šubnikov, Aleksej V. 1887-1970 |
| author_variant | a v š av avš n v b nv nvb |
| building | Verbundindex |
| bvnumber | BV005686107 |
| classification_rvk | UQ 1300 VE 5700 |
| ctrlnum | (OCoLC)612726365 (DE-599)BVBBV005686107 |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01557nam a2200349 c 4500</leader><controlfield tag="001">BV005686107</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20030213 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">921028s1964 ad|| |||| 00||| eng d</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)612726365</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005686107</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UQ 1300</subfield><subfield code="0">(DE-625)146478:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">VE 5700</subfield><subfield code="0">(DE-625)147119:253</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Šubnikov, Aleksej V.</subfield><subfield code="d">1887-1970</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)117462055</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Simmetrija i antisimmetrija konečnych figur</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Colored symmetry</subfield><subfield code="b">a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958</subfield><subfield code="c">by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford [u.a.]</subfield><subfield code="b">Pergamon Press</subfield><subfield code="c">1964</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXV, 263 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kristallsymmetrie</subfield><subfield code="0">(DE-588)4136175-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kristallsymmetrie</subfield><subfield code="0">(DE-588)4136175-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Belov, Nikolaj V.</subfield><subfield code="d">1891-1982</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)134216539</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Holser, William T.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003551535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003551535</subfield></datafield></record></collection> |
| id | DE-604.BV005686107 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:08Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003551535 |
| oclc_num | 612726365 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 |
| physical | XXV, 263 S. Ill., graph. Darst. |
| publishDate | 1964 |
| publishDateSearch | 1964 |
| publishDateSort | 1964 |
| publisher | Pergamon Press |
| record_format | marc |
| spelling | Šubnikov, Aleksej V. 1887-1970 Verfasser (DE-588)117462055 aut Simmetrija i antisimmetrija konečnych figur Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser Oxford [u.a.] Pergamon Press 1964 XXV, 263 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kristallsymmetrie (DE-588)4136175-1 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 s DE-604 Belov, Nikolaj V. 1891-1982 Verfasser (DE-588)134216539 aut Holser, William T. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003551535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šubnikov, Aleksej V. 1887-1970 Belov, Nikolaj V. 1891-1982 Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 Kristallsymmetrie (DE-588)4136175-1 gnd |
| subject_GND | (DE-588)4136175-1 |
| title | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 |
| title_alt | Simmetrija i antisimmetrija konečnych figur |
| title_auth | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 |
| title_exact_search | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 |
| title_full | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser |
| title_fullStr | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser |
| title_full_unstemmed | Colored symmetry a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 by A. V. Shubnikov, N.V. Belov. Ed. by William T. Holser |
| title_short | Colored symmetry |
| title_sort | colored symmetry a series of publications from the institute of crystallography academy of sciences of the u s s r moscow 1951 1958 |
| title_sub | a series of publications from the Institute of Crystallography Academy of Sciences of the U.S.S.R., Moscow, 1951 - 1958 |
| topic | Kristallsymmetrie (DE-588)4136175-1 gnd |
| topic_facet | Kristallsymmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003551535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT subnikovaleksejv simmetrijaiantisimmetrijakonecnychfigur AT belovnikolajv simmetrijaiantisimmetrijakonecnychfigur AT holserwilliamt simmetrijaiantisimmetrijakonecnychfigur AT subnikovaleksejv coloredsymmetryaseriesofpublicationsfromtheinstituteofcrystallographyacademyofsciencesoftheussrmoscow19511958 AT belovnikolajv coloredsymmetryaseriesofpublicationsfromtheinstituteofcrystallographyacademyofsciencesoftheussrmoscow19511958 AT holserwilliamt coloredsymmetryaseriesofpublicationsfromtheinstituteofcrystallographyacademyofsciencesoftheussrmoscow19511958 |