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Bibliographic Details
Main Author:	Johnson, David L. 1943- (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Springer 2001
Series:	Springer undergraduate mathematics series
Subjects:	Symmetry groups Symmetrische Gruppe Symmetrie
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XI, 198 S. Ill., graph. Darst.
ISBN:	1852332700

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adam_text	Contents 1. Metric Spaces and their Groups.................................. 1 1.1 Metric Spaces.............................................. 1 1.2 Isometries................................................. 4 1.3 Isometries of the Real Line ............................... 5 1.4 Matters Arising............................................ 7 1.5 Symmetry Groups........................................... 10 2. Isometries of the Plane........................................ 15 2.1 Congruent Triangles....................................... 15 2.2 Isometries of Different Types............................. 18 2.3 The Normal Form Theorem................................... 20 2.4 Conjugation of Isometries ................................ 21 3. Some Basic Group Theory........................................ 27 3.1 Groups.................................................... 28 3.2 Subgroups................................................. 30 3.3 Factor Groups ............................................ 33 3.4 Semidirect Products....................................... 36 4. Products of Reflections........................................ 45 4.1 The Product of Two Reflections............................ 45 4.2 Three Reflections......................................... 47 4.3 Four or More.............................................. 50 5. Generators and Relations....................................... 55 5.1 Examples.................................................. 56 5.2 Semidirect Products Again ................................ 60 ix x Contents 5.3 Change of Presentation...................................... 65 5.4 Triangle Groups............................................. 69 5.5 Abelian Groups.............................................. 70 6. Discrete Subgroups of the Euclidean Group ........................ 79 6.1 Leonardo’s Theorem........................................... 80 6.2 A Trichotomy................................................. 81 6.3 Friezes and Their Groups.................................... 83 6.4 The Classification.......................................... 85 7. Plane Crystallographic Groups: OP Case............................ 89 7.1 The Crystallographic Restriction............................. 89 7.2 The Parameter .............................................. 01 7.3 The Choice of b.............................................. 92 7.4 Conclusion ................................................. 94 8. Plane Crystallographic Groups: OR Case............................ 97 8.1 A Useful Dichotomy........................................... 97 8.2 The Case n = 1...............................................190 8.3 The Case n = 2...............................................190 8.4 The Case n — 4...............................................101 8.5 The Case n = 3...............................................102 8.6 The Case n = 6...............................................104 9. Tessellations of the Plane.........................................107 9.1 Regular Tessellations........................................107 9.2 Descendants of (4, 4) ........................................HO 9.3 Bricks.......................................................112 9.4 Split Bricks.................................................113 9.5 Descendants of (3, 6) .......................................116 10« Tessellations of the Sphere........................................123 10.1 Spherical Geometry...........................................123 10.2 The Spherical Excess ........................................125 10.3 Tessellations of the Sphere..................................128 10.4 The Platonic Solids..........................................130 10.5 Symmetry Groups...........................................133 11 11. Triangle Groups...................................................139 11.1 The Euclidean Case..........................................140 11.2 The Elliptic Case...........................................142 11.3 The Hyperbolic Case.........................................144 Contents Xf 11.4 Coxeter Groups.......................................... 146 12. Regular Poly topes.............................................155 12.1 The Standard Examples.....................................156 12.2 The Exceptional Types in Dimension Four...................158 12.3 Three Concepts and a Theorem..............................160 12.4 Schlafli’s Theorem........................................163 Solutions..........................................................167 Guide to the Literature............................................187 Bibliography.......................................................189 Index of Notation .................................................191 Index 195
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dewey-tens	510 - Mathematics
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illustrated	Illustrated
indexdate	2024-07-09T18:50:56Z
institution	BVB
isbn	1852332700
language	English
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physical	XI, 198 S. Ill., graph. Darst.
publishDate	2001
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publisher	Springer
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series2	Springer undergraduate mathematics series
spelling	Johnson, David L. 1943- Verfasser (DE-588)115496629 aut Symmetries D. L. Johnson London [u.a.] Springer 2001 XI, 198 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Hier auch später erschienene, unveränderte Nachdrucke Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Symmetrie (DE-588)4058724-1 s DE-604 Symmetrische Gruppe (DE-588)4184204-2 s Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009382477&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Johnson, David L. 1943- Symmetries Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd Symmetrie (DE-588)4058724-1 gnd
subject_GND	(DE-588)4184204-2 (DE-588)4058724-1
title	Symmetries
title_auth	Symmetries
title_exact_search	Symmetries
title_full	Symmetries D. L. Johnson
title_fullStr	Symmetries D. L. Johnson
title_full_unstemmed	Symmetries D. L. Johnson
title_short	Symmetries
title_sort	symmetries
topic	Symmetry groups Symmetrische Gruppe (DE-588)4184204-2 gnd Symmetrie (DE-588)4058724-1 gnd
topic_facet	Symmetry groups Symmetrische Gruppe Symmetrie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009382477&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT johnsondavidl symmetries

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