| 释义 |
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In mathematics, a rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups. This constraint means that the point group must be the symmetry of some three-dimensional lattice. Table of the 75 rod groups, organized by crystal system or lattice type, and by their point groups: | Triclinic | | 1 | p1 | 2 | 1}} |
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| Monoclinic/inclined |
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| 3 | p211 | 4 | pm11 | 5 | pc11 | 6 | p2/m11 | 7 | p2/c11 |
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| Monoclinic/orthogonal |
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| 8 | p112 | 9 | p1121 | 10 | p11m | 11 | p112/m | 12 | p1121/m |
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| Orthorhombic |
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| 13 | p222 | 14 | p2221 | 15 | pmm2 | 16 | pcc2 | 17 | pmc21 |
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| 18 | p2mm | 19 | p2cm | 20 | pmmm | 21 | pccm | 22 | pmcm |
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| Tetragonal |
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| 23 | p4 | 24 | p41 | 25 | p42 | 26 | p43 | 27 | 4}} |
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| 28 | p4/m | 29 | p42/m | 30 | p422 | 31 | p4122 | 32 | p4222 |
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| 33 | p4322 | 34 | p4mm | 35 | p42cm, p42mc | 36 | p4cc | 37 | 4}}2m, p{{overline|4}}m2 |
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| 38 | 4}}2c, p{{overline|4}}c2 | 39 | p4/mmm | 40 | p4/mcc | 41 | p42/mmc, p42/mcm |
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| Trigonal |
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| 42 | p3 | 43 | p31 | 44 | p32 | 45 | 3}} | 46 | p312, p321 |
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| 47 | p3112, p3121 | 48 | p3212, p3221 | 49 | p3m1, p31m | 50 | p3c1, p31c | 51 | 3}}m1, p{{overline|3}}1m |
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| 52 | 3}}c1, p{{overline|3}}1c |
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| Hexagonal |
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| 53 | p6 | 54 | p61 | 55 | p62 | 56 | p63 | 57 | p64 |
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| 58 | p65 | 59 | 6}} | 60 | p6/m | 61 | p63/m | 62 | p622 |
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| 63 | p6122 | 64 | p6222 | 65 | p6322 | 66 | p6422 | 67 | p6522 |
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| 68 | p6mm | 69 | p6cc | 70 | p63mc, p63cm | 71 | 6}}m2, p{{overline|6}}2m | 72 | 6}}c2, p{{overline|6}}2c |
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| 73 | p6/mmm | 74 | p6/mcc | 75 | p6/mmc, p6/mcm |
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The double entries are for orientation variants of a group relative to the perpendicular-directions lattice. Among these groups, there are 8 enantiomorphic pairs. See also - Point group
- Crystallographic point group
- Space group
- Line group
- Frieze group
- Layer group
References - {{Citation | last1=Hitzer | first1=E.S.M. | last2=Ichikawa | first2=D. | title=Representation of crystallographic subperiodic groups by geometric algebra | url=http://sinai.apphy.u-fukui.ac.jp/gcj/publications/RCSGGA/RCSGGA.pdf | journal=Electronic Proc. of AGACSE | issue=3, 17–19 Aug. 2008 | location=Leipzig, Germany | year=2008 | deadurl=yes | archiveurl=https://web.archive.org/web/20120314155923/http://sinai.apphy.u-fukui.ac.jp/gcj/publications/RCSGGA/RCSGGA.pdf | archivedate=2012-03-14 | df= }}
- {{Citation | editor1-last=Kopsky | editor1-first=V. | editor2-last=Litvin | editor2-first=D.B. | title=International Tables for Crystallography, Volume E: Subperiodic groups | url=http://it.iucr.org/E/ | publisher=Springer-Verlag | location=Berlin, New York | edition=5th | isbn=978-1-4020-0715-6 |doi= 10.1107/97809553602060000105 | year=2002 | volume=E}}
External links - Bilbao Crystallographic Server, under "Subperiodic Groups: Layer, Rod and Frieze Groups"
- Nomenclature, Symbols and Classification of the Subperiodic Groups, V. Kopsky and D. B. Litvin
2 : Euclidean symmetries|Discrete groups |