560 



Ab- 



Sym- 

 metrie- 

 art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Symbol 

 des Systems 



leitungs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



abc 



8. 



8 



1 



vxvi 



15' 



a = 1'5 b = 2'6 c = 



2 6' 



2(;i;6)(l^VI,) 



abc 



8 



8 



2 





15' 



rt = 1'5 h = 26' c = 



2'6 



4;i;3(l5rVI,) 



abc 



8 



8 



3 



)) 



1 5' 



n = 2'6 ö= 1'5 c = 



2 6' 



14(/2)(l.-rVl7) 



ahc 



8 



8 



4 



)J 



12' 



a = 5 6' ö = 5'6 c = 



1'2 



3 (x 3) (3 VI,) 



ab c 



8 



8 



5 



)) 



12' 



a == 5 6' & = 1'2 c = 



5'6 



3 (z 4) (3 VI,) 



ab c 



8 



8 



6 



)) 



1 2' 



a = 5'6 & = 1'2 c = 



5 6' 



2 U 5) (3 VI,) 



a a 



8 



8 



7 



" 



1 2' 



« 5 6, 



- = ^Tir b = 1 2 



rt 5 b 





5(;^2)(3VI,)5y 



a a 

 a' a' 



• 8 



8 



8 



» 



16' 



a 2'5 

 o' 2 5' 





5x3{3VI,)^2' 



abc 



8 



8 



9 



)) 



1 1' 



a = 5 5' & = 6 6' c = 



2 2' 



4z KU' VI,) 



abc 



8 



8 



10 



jj 



1 l' 



a = 5 5' h = 22' c = 



6 6' 



2(z4)(lz'VI,) 



abc 



8 



8 



11 



j, 



1 1' 



a = 6 6' b = 5 5' c = 



2 2' 



2 (x 2) dz' VI,) 



abc 



8 



8 



12 



,, 



1 1' 



a = 6 6' & = 2 2'c = 



5 5' 



14 UD dz' VI,) 



a a 

 a a 



8 



8 



13 



)> 



1 1' 



a 5 5' 

 a' 2 2' 





4(z2)(lz'VI,)-^5 



a a' , 

 -, — b 

 a a 



8 



8 



14 



" 



1 1' 



rt' 6 6' 



7 All 





6zl(lz'VI,)56 



b b 

 b b 



8 



8 



15 



6z VI 



1 1' 



o c '^ 4 4' 



« = 8 8' =-r = rT7 



h 5 5 





14(zl)(lz'Vl6)l5 



b b' 



8 



8 



16 





18' 



.';. ^ 4 5' 



" = ^^ F = r8 





7zl(3VV)i,^ 



l^b_ 

 V V 



8 



8 



17 





15 



b Vb' 



V ~ 4'8' 





2(z6)(3VI6)^4, 



b V 

 ^Fb 



8 



8 



18 





15 



,w h 1'5' 



« = 4 8 77 = -— 



h' 4 8 





7zl(3Vl6),.4 



b_l^ 



b' V 



8 



8 



19 





14 



h 1'4' 

 V 5'8' 





14(zl)(lz'Vl6')l-5- 



bb: 



b'b 



8 



8 



20 





14 



h 58 

 V 5'8' 





14(zl)(lz'VV)^5' 



b^b^ 



8 



8 



21 





14' 



h 5'8 

 h' 5 8' 





2(z6)(3VV)^5, 



a a a 

 a' a' a' 



8 



8 



1 



6/ VII 



16' 



rt _25' 

 rt' ~ 1'6 





7zl(3VIl6)i,2 



a a' a 



8 



8 



2 





16' 



rt _25' 





2(z6)(3VIl6)52- 



a' a a' 













rt' 2'5 







a a' a 



8 



8 



3 





1 1' 



a 2 2' 





14(zl)(lz'VIl6)|5 



a' a a' 













rt' 55' 







a b b 



8 



8 



4 



7/ VII 



15' 



a = 4'8 h = 1'5 





2(z6)(l^VII,)o 



abh 



8 



8 



5 



)) 



15' 



rt = 4'8 h = 4:8' 





4z3(l.T VII,)« 



ah h 



8 



8 



6 





15' 



a = 4 8' h = l'6 





14(/2)(ljrVII,)<= 



abh. 



8 



8 



7 



)j 



15' 



« = 48' h = 4'8 





2(z6)(lJiVIl7)'^ 



abh 



8 



8 



8 



») 



18' 



a=l'8 b = 4'5 





2 (z 5) (3 VII,')« 



abh 



8 



8 



9 





14' 



« = 5'8 & = 5 8' 





3(z4){3VII,')« 



abh 



8 



8 



10 



)) 



18' 



a = 1'8 b = 4 5' 





3(z4)(3VIV)=' 



a h h 



8 



8 



11 





18' 



«=45' b = 4'5 





2(z5)(3VII,')^' 



ab b 



8 



8 



12 



„ 



14' 



a = 1'4 6 = 5 8' 





3 {/ 3) (3 VII,')<^ 



abh 



8 



8 



13 



}} 



18' ■ 



a = 4 5' 6 = 1'8 





3(z3)(3VlI,'K 



a h h 



8 



8 



14 





1 1' 



n = 88' b = 55' 





14(zl)(lz'VIl7)'' 



a b h 



8 



8 



15 



,, 



1 1' 



a = 8 8' b = 4 4' 





2(z-t){lz'Vll7)'= 



abh 



8 



8 



16 



,, 



11' 



a = 4 4' b = 5 5' 





2 (z 2) dz' VII,)'' 



ah b 



8 



8 



17 



)) 



. 1 1' 



a = 4 4' b = 8 8' 





4z 1 dz' VII,)« 



« 7 7 



a 



8 



8 



18 



)» 



1 1' 



« 4 4' , 



-i = r^ b = 88' 



rt 5 5 





6zldz'VIl7)45 



a 

 -, 1 1 



8 



8 



19 





18' 



a 4'5 





5 z 3 {3 VII,')4 4' 



a 













a' ~ 4 5' 







