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:
Hitzer, E.S.M.; Ichikawa, D. (2008), (PDF), Electronic Proc. Of AGACSE, Leipzig, Germany (3, 17–19 Aug. 2008), archived from the original (PDF) on 2012-03-14
Kopsky, V.; Litvin, D.B., eds. (2002), International Tables for Crystallography, Volume E: Subperiodic groups, International Tables for Crystallography, vol. E (5th ed.), Berlin, New York: Springer-Verlag, doi:10.1107/97809553602060000105, ISBN978-1-4020-0715-6
Nomenclature, Symbols and Classification of the Subperiodic Groups, V. Kopsky and D. B. Litvin
January 06, 2023
group, mathematics, group, three, dimensional, line, group, whose, point, group, axial, crystallographic, point, groups, this, constraint, means, that, point, group, must, symmetry, some, three, dimensional, lattice, table, groups, organized, crystal, system, . 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 Triclinic1 p1 2 p1Monoclinic inclined3 p211 4 pm11 5 pc11 6 p2 m11 7 p2 c11Monoclinic orthogonal8 p112 9 p1121 10 p11m 11 p112 m 12 p1121 mOrthorhombic13 p222 14 p2221 15 pmm2 16 pcc2 17 pmc2118 p2mm 19 p2cm 20 pmmm 21 pccm 22 pmcmTetragonal23 p4 24 p41 25 p42 26 p43 27 p428 p4 m 29 p42 m 30 p422 31 p4122 32 p422233 p4322 34 p4mm 35 p42cm p42mc 36 p4cc 37 p4 2m p4 m238 p4 2c p4 c2 39 p4 mmm 40 p4 mcc 41 p42 mmc p42 mcmTrigonal42 p3 43 p31 44 p32 45 p3 46 p312 p32147 p3112 p3121 48 p3212 p3221 49 p3m1 p31m 50 p3c1 p31c 51 p3 m1 p3 1m52 p3 c1 p3 1cHexagonal53 p6 54 p61 55 p62 56 p63 57 p6458 p65 59 p6 60 p6 m 61 p63 m 62 p62263 p6122 64 p6222 65 p6322 66 p6422 67 p652268 p6mm 69 p6cc 70 p63mc p63cm 71 p6 m2 p6 2m 72 p6 c2 p6 2c73 p6 mmm 74 p6 mcc 75 p63 mmc p63 mcmThe 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 EditPoint group Crystallographic point group Space group Line group Frieze group Layer groupReferences EditHitzer E S M Ichikawa D 2008 Representation of crystallographic subperiodic groups by geometric algebra PDF Electronic Proc Of AGACSE Leipzig Germany 3 17 19 Aug 2008 archived from the original PDF on 2012 03 14 Kopsky V Litvin D B eds 2002 International Tables for Crystallography Volume E Subperiodic groups International Tables for Crystallography vol E 5th ed Berlin New York Springer Verlag doi 10 1107 97809553602060000105 ISBN 978 1 4020 0715 6External links Edit Subperiodic Groups Layer Rod and Frieze Groups on Bilbao Crystallographic Server Nomenclature Symbols and Classification of the Subperiodic Groups V Kopsky and D B Litvin Retrieved from https en wikipedia org w index php title Rod group amp oldid 1114254709, wikipedia, wiki, book, books, library,
