Difference between revisions of "Template:List space groups Coxeter notation"

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imported>Tomruen
imported>WOSlinker
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{| class="wikitable collapsible collapsed"
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{| class="wikitable mw-collapsible mw-collapsed"
 
!colspan=12|Rank four groups as 3-dimensional [[space group]]s
 
!colspan=12|Rank four groups as 3-dimensional [[space group]]s
 
|- style="vertical-align:top;text-align:center;"
 
|- style="vertical-align:top;text-align:center;"
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|[∞,2,∞,2,∞]<sup>+</sup>||(16) P222
 
|[∞,2,∞,2,∞]<sup>+</sup>||(16) P222
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[∞,2,∞,2,∞]]<sup>+</sup>||(23) I222
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|[<nowiki/>[∞,2,∞,2,∞]]<sup>+</sup>||(23) I222
 
|- style="text-align:center;"
 
|- style="text-align:center;"
 
|[∞<sup>+</sup>,2,∞,2,∞]||(25) Pmm2
 
|[∞<sup>+</sup>,2,∞,2,∞]||(25) Pmm2
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|[∞,2,∞,2,∞]||(47) Pmmm
 
|[∞,2,∞,2,∞]||(47) Pmmm
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[∞,2,∞,2,∞]]||(71) Immm
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|[<nowiki/>[∞,2,∞,2,∞]]||(71) Immm
 
|- style="text-align:center;"
 
|- style="text-align:center;"
 
|[∞<sup>+</sup>,2,∞<sup>+</sup>,2,∞<sup>+</sup>]||
 
|[∞<sup>+</sup>,2,∞<sup>+</sup>,2,∞<sup>+</sup>]||
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!Index
 
!Index
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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!rowspan=9|[</span>[4,3,4]]
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!rowspan=9|[<nowiki/>[4,3,4]]
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|[</span>[4,3,4]]||(229) Im{{overline|3}}m||1
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|[<nowiki/>[4,3,4]]||(229) Im{{overline|3}}m||1
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[4,3,4]]<sup>+</sup>||(211) I432||2
+
|[<nowiki/>[4,3,4]]<sup>+</sup>||(211) I432||2
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[4,3,4]<sup>+</sup>]||(223) Pm{{overline|3}}n||2
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|[<nowiki/>[4,3,4]<sup>+</sup>]||(223) Pm{{overline|3}}n||2
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[4,3<sup>+</sup>,4]]||(204) I{{overline|3}}||2
+
|[<nowiki/>[4,3<sup>+</sup>,4]]||(204) I{{overline|3}}||2
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[(4,3,4,2<sup>+</sup>)]]||(217) I{{overline|4}}3m ||2
+
|[<nowiki/>[(4,3,4,2<sup>+</sup>)]]||(217) I{{overline|4}}3m ||2
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[4,3<sup>+</sup>,4]]<sup>+</sup>||(197) I23 ||4
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|[<nowiki/>[4,3<sup>+</sup>,4]]<sup>+</sup>||(197) I23 ||4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[4,3,4]<sup>+</sup>]<sup>+</sup>||(208) P4<sub>2</sub>32||4
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|[<nowiki/>[4,3,4]<sup>+</sup>]<sup>+</sup>||(208) P4<sub>2</sub>32||4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[4,3<sup>+</sup>,4)]<sup>+</sup>]||(201) Pn{{overline|4}}3||4
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|[<nowiki/>[4,3<sup>+</sup>,4)]<sup>+</sup>]||(201) Pn{{overline|4}}3||4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
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|[</span>[(4,3,4,2<sup>+</sup>)]<sup>+</sup>]||(218) P{{overline|4}}3n||4
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|[<nowiki/>[(4,3,4,2<sup>+</sup>)]<sup>+</sup>]||(218) P{{overline|4}}3n||4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
 
!rowspan=8|[4,3,4]<BR>{{CDD|node|4|node|3|node|4|node}}
 
!rowspan=8|[4,3,4]<BR>{{CDD|node|4|node|3|node|4|node}}
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|[(4,3,4,2<sup>+</sup>)]||(215) P{{overline|4}}3m||4
 
|[(4,3,4,2<sup>+</sup>)]||(215) P{{overline|4}}3m||4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[{4,(3}<sup>+</sup>,4)<sup>+</sup>]]|| (228) Fd{{overline|3}}c || 4
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|[<nowiki/>[{4,(3}<sup>+</sup>,4)<sup>+</sup>]]|| (228) Fd{{overline|3}}c || 4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
 
|[4,3<sup>+</sup>,4]<sup>+</sup>||(195) P23||8
 
|[4,3<sup>+</sup>,4]<sup>+</sup>||(195) P23||8
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|- style="text-align:center;"
 
|- style="text-align:center;"
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!rowspan=5|[</span>[3<sup>[4]</sup>]]<BR>{{CDD|branch|3ab|branch}}
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!rowspan=5|[<nowiki/>[3<sup>[4]</sup>]]<BR>{{CDD|branch|3ab|branch}}
 
|- style="text-align:center;"
 
|- style="text-align:center;"
 
|[(4<sup>+</sup>,2<sup>+</sup>)[3<sup>[4]</sup>]] ||(222) Pn{{overline|3}}n || 2
 
|[(4<sup>+</sup>,2<sup>+</sup>)[3<sup>[4]</sup>]] ||(222) Pn{{overline|3}}n || 2
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[3<sup>[4]</sup>]] || (227) Fd{{overline|3}}m || 4
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|[<nowiki/>[3<sup>[4]</sup>]] || (227) Fd{{overline|3}}m || 4
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[3<sup>[4]</sup>]]<sup>+</sup> ||(203) Fd{{overline|3}}|| 8
+
|[<nowiki/>[3<sup>[4]</sup>]]<sup>+</sup> ||(203) Fd{{overline|3}}|| 8
 
|- style="text-align:center;"
 
|- style="text-align:center;"
−
|[</span>[3<sup>[4]</sup>]<sup>+</sup>] ||(210) F4<sub>1</sub>32 || 8
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|[<nowiki/>[3<sup>[4]</sup>]<sup>+</sup>] ||(210) F4<sub>1</sub>32 || 8
  
 
|- style="text-align:center;"
 
|- style="text-align:center;"

Latest revision as of 19:17, 25 February 2021

Rank four groups as 3-dimensional space groups
Triclinic (1-2)
Coxeter Space group
[∞+,2,∞+,2,∞+] (1) P1
Monoclinic (3-15)
Coxeter Space group
[(∞,2,∞)+,2,∞+] (3) P2
[∞+,2,∞+,2,∞] (6) Pm
[(∞,2,∞)+,2,∞] (10) P2/m
Orthorhombic (16-74)
File:CDel node.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png
Coxeter Space group
[∞,2,∞,2,∞]+ (16) P222
[[∞,2,∞,2,∞]]+ (23) I222
[∞+,2,∞,2,∞] (25) Pmm2
[∞,2,∞,2,∞] (47) Pmmm
[[∞,2,∞,2,∞]] (71) Immm
[∞+,2,∞+,2,∞+]
[∞,2,∞,2+,∞]
[∞,2+,∞,2+,∞]
Tetragonal (75-142)
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png
Coxeter Space group
[(4,4)+,2,∞+] (75) P4
[2+[(4,4)+,2,∞+]] (79) I4
[(4,4)+,2,∞] (83) P4/m
[2+[(4,4)+,2,∞]] (87) I4/m
[4,4,2,∞]+ (89) P422
[2+[4,4,2,∞]]+ (97) I422
[4,4,2,∞+] (99) P4mm
[4,4,2,∞] (123) P4/mmm
[2+[4,4,2,∞]] (139) I4/mmm
[4,(4,2)+,∞] (140) I4/mcm
[4,4,2+,∞]
[(4,4)+,2+,∞]
[4,4,2+,∞+]
[(4,4)+,2+,∞+]
[4+,4+,2+,∞]
[4,4+,2,∞]
[4,4+,2+,∞]
[((4,2+,4)),2,∞]
[4,4+,2,∞+]
[4,4+,2+,∞+]
[((4,2+,4)),2,∞+]
Trigonal (143-167), rhombohedral
Coxeter Space group
Hexagonal (168-194)
File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 6.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node.pngFile:CDel infin.pngFile:CDel node.png
[(6,3)+,2,∞+] (168) P6
[(6,3)+,2,∞] (175) P6/m
[6,3,2,∞]+ (177) P622
[6,3,2,∞+] (183) P6mm
[6,3,2,∞] (191) P6/mmm
[(3[3])+,2,∞+]
[3[3],2,∞]
[6,3+,2,∞]
[6,3+,2,∞+]
[3[3],2,∞]+
[3[3],2,∞+]
[(3[3])+,2,∞]
Cubic (195-230)
Group Coxeter Space group Index
[[4,3,4]] [[4,3,4]] (229) ImTemplate:Overlinem 1
[[4,3,4]]+ (211) I432 2
[[4,3,4]+] (223) PmTemplate:Overlinen 2
[[4,3+,4]] (204) ITemplate:Overline 2
[[(4,3,4,2+)]] (217) ITemplate:Overline3m 2
[[4,3+,4]]+ (197) I23 4
[[4,3,4]+]+ (208) P4232 4
[[4,3+,4)]+] (201) PnTemplate:Overline3 4
[[(4,3,4,2+)]+] (218) PTemplate:Overline3n 4
[4,3,4]
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png 		[4,3,4] (221) PmTemplate:Overlinem 2
[4,3,4]+ (207) P432 4
[4,3+,4] (200) PmTemplate:Overline 4
[4,(3,4)+] (226) FmTemplate:Overlinec 4
[(4,3,4,2+)] (215) PTemplate:Overline3m 4
[[{4,(3}+,4)+]] (228) FdTemplate:Overlinec 4
[4,3+,4]+ (195) P23 8
[{4,(3}+,4)+] (219) FTemplate:Overline3c 8
[4,31,1]
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel split1.pngFile:CDel nodes.png
File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h0.png 		[4,31,1] (225) FmTemplate:Overlinem 4
[4,(31,1)+] (202) FmTemplate:Overline 8
[4,31,1]+ (209) F432 8
[[3[4]]]
File:CDel branch.pngFile:CDel 3ab.pngFile:CDel branch.png
[(4+,2+)[3[4]]] (222) PnTemplate:Overlinen 2
[[3[4]]] (227) FdTemplate:Overlinem 4
[[3[4]]]+ (203) FdTemplate:Overline 8
[[3[4]]+] (210) F4132 8
[3[4]]
File:CDel branch.pngFile:CDel 3ab.pngFile:CDel branch.png
File:CDel node h0.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node h0.png 		[3[4]] (216) FTemplate:Overline3m 8
[3[4]]+ (196) F23 16
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