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Rod group

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:

class="wikitable"

! colspan=10 | Triclinic

1

| p1

!2

| p{{overline|1}}

colspan=10 | Monoclinic/inclined
3

| p211

!4

| pm11

!5

| pc11

!6

| p2/m11

!7

| p2/c11

colspan=10 | Monoclinic/orthogonal
8

| p112

!9

| p1121

!10

| p11m

!11

| p112/m

!12

| p1121/m

colspan=10 | Orthorhombic
13

| p222

!14

| p2221

!15

| pmm2

!16

| pcc2

!17

| pmc21

18

| p2mm

!19

| p2cm

!20

| pmmm

!21

| pccm

!22

| pmcm

colspan=10 | Tetragonal
23

| p4

!24

| p41

!25

| p42

!26

| p43

!27

| p{{overline|4}}

28

| p4/m

!29

| p42/m

!30

| p422

!31

| p4122

!32

| p4222

33

| p4322

!34

| p4mm

!35

| p42cm, p42mc

!36

| p4cc

!37

| p{{overline|4}}2m, p{{overline|4}}m2

38

| p{{overline|4}}2c, p{{overline|4}}c2

!39

| p4/mmm

!40

| p4/mcc

!41

| p42/mmc, p42/mcm

colspan=10 | Trigonal
42

| p3

!43

| p31

!44

| p32

!45

| p{{overline|3}}

!46

| p312, p321

47

| p3112, p3121

!48

| p3212, p3221

!49

| p3m1, p31m

!50

| p3c1, p31c

!51

| p{{overline|3}}m1, p{{overline|3}}1m

52

| p{{overline|3}}c1, p{{overline|3}}1c

colspan=10 | Hexagonal
53

| p6

!54

| p61

!55

| p62

!56

| p63

!57

| p64

58

| p65

!59

| p{{overline|6}}

!60

| p6/m

!61

| p63/m

!62

| p622

63

| p6122

!64

| p6222

!65

| p6322

!66

| p6422

!67

| p6522

68

| p6mm

!69

| p6cc

!70

| p63mc, p63cm

!71

| p{{overline|6}}m2, p{{overline|6}}2m

!72

| p{{overline|6}}c2, p{{overline|6}}2c

73

| p6/mmm

!74

| p6/mcc

!75

| p6{{sub|3}}/mmc, p6{{sub|3}}/mcm

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

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 | url-status=dead | archiveurl=https://web.archive.org/web/20120314155923/http://sinai.apphy.u-fukui.ac.jp/gcj/publications/RCSGGA/RCSGGA.pdf | archivedate=2012-03-14 }}
  • {{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| url-access=subscription }}

External links

  • [http://www.cryst.ehu.es/ "Subperiodic Groups: Layer, Rod and Frieze Groups"] on Bilbao Crystallographic Server
  • [http://www.bk.psu.edu/faculty/litvin/Download/D_IUCr_Report.pdf Nomenclature, Symbols and Classification of the Subperiodic Groups, V. Kopsky and D. B. Litvin]

Category:Euclidean symmetries

Category:Discrete groups