534 



Ab- 



Sym- 

 metrie- 

 art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Symbol 

 des Systems 



leitungs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



a 



12 



8 



8 



8x111 



15 



a 3'7' 

 a' " 1'5' 



6 ix 1) (2 III)'i,3, 



a 



12 



8 



9 



.. 



15 



a 15 



9x (2 111)1,3, 



\h c 



12 



8 



10 



,, 



1 1' 



b = 3 3' c = 7 7' 



sxdziii) 



ah c 



12 



8 



11 



,, 



11' 



fe=3 3'c = 7 7' a = 5 5' 



9/ dz III) 



ahh 



13 



8 



1 



10 III 



15 



a = 3 7 ?) = 2'6' 



• (18) (2 III) 



abb 



13 



8 



2 



„ 



15 



a = 3 7 & = 4'8' 



(18) (2 III)' 



abb 



13 



8 



3 



^J 



15 



a = 2'6' ö = 3 7 



(7) (2 III) 



ab b 



13 



8 



4 



)» 



15 



a = 2'6' & = 4'8' 



(1Ö)(2III)" 



abb 



13 



8 



5 





15 



a = 4'8' & = 3 7 



10 (2 III) 



abb 



13 



8 



6 





15 



a = 4'8' h = 2'6' 



(8) (2 III) 



-,11 

 a 



13 



8 



7 



" 



15 



a 2'6' 



a' ~ 4'8' 



(8) (2 III)^2'4' 



'^,bh 

 a 



13 



8 



8 



„ 



1 5 



« 2'6' , 



a' 4'8 



11(2111)2-4- 



a 



13 



8 



9 



" 



12' 



a 7 8' 

 a' ~ 3 4' 



(19)(2II1); 



^11 

 a 



13 



8 



10 



" 



12' 



a 3 4' 

 a' ~ 7 8' 



(20) (2 lll)i' 



« 7 I, 



—,bb 

 a 



13 



8 



11 



" 



12' 



^-ü:'-- 



(21) (2 III), 



« 7 7, 



13 



8 



12 



JJ 



12' 



?-?^=« 



(21)(2III)i 



1 hc 



13 



8 



13 



)) 



14' 



b = 3 6' c = 2'7 



(7) (3 III)= 



1 bc 



13 



8 



14 



J) 



14' 



6 = 2'7 c = 3 6' o'7 

 rt = 5 8' b = 3 6' ^ Z Q fi, 

 a = 5 8' b = 2'7 <^ - ^ "^ 



10 (3 111)*= 



ab c 

 abc 



13 

 13 



8 

 8 



15 



16 





14' 

 14' 



11(3111) 

 11(3111)' 



a 



13 



8 



17 



)) 



14' 



a 2'7 

 a' ~ 3 6' 



(19) (3 III)^ 



--11 

 a 



13 



8 



18 



" 



14' 



a 3 6' 



a' ~ 2'7 



(20) (3 IIDJ 



« J 7, 



a 



13 



8 



19 



M 



14' 



i-ri'--' 



(21)(:tiIII), 



%bb 

 a 



13 



8 



20 



' 



14' 



I = It'--' 



(21) (3111)^ 



ab b 



14 



8 



1 



4ÖIII 



15 



a = 3'7' b = 2'6' 



5 <5 3 (2 III) 



abb 



14 



8 



2 



„ 



15 



a = 3'7' b = 48 



5^2(2111) 



abb 



14 



8 



3 



„ 



15 



a = 2'6' b = 3'7' 



5 03(2 111)' 



abb 



14 



8 



4 



„ 



15 



a = 2'6' = 48 



5 52(2111)' 



abb 



14 



8 



5 



,, 



15 



a = 48 & = 3'7' 



5(51(2111) 



ab b- 



14 



8 



6 



„ 



15 



a = 4 8 & = 2'6' 



5.51(2111)' 



a 



14 



8 



7 



" 



15 



o 3'7' 

 a' ~ 2'6' 



4<51(2111)'2,3- 



« 7 k 



—,bb 

 a 



14 



8 



8 



)J 



15 



'=2^ = 48 

 a' 2'6' 



552(2111)2,3, 



Ibc 



14 



8 



9 



)J 



18 . 



b = 2'3' c = 6'7' 



4ö(lx'IIl)'= 



1 bc 



14 



8 



10 





18 



b = 6'7' c = 2'3' 



2 (5 1) (1 z' 111)'^ 



abc 



14 



8 



11 



)J 



18 



a = 4 5 b = 2'3' c = ß'y' 



65(1/'III) 



abc 



14 



8 



12 



)J 



18 



a = 4 5 6 = 6'7' c = 2'3' 



65 dz' 111)' 



abb 



14 



8 



13 



5 5 III 



15 



a = 3'7' b = 26 



2 (51) (2 III) 



abb 



14 



8 



14 



jj 



15 



a = 3'7' b = 4'8' 



2 (52) (2 III) 



abb 



14 



8 



15 



n 



15 



a=2 6 b = 3'7' 



2 (5 2) (2 111)' 



abb 



14 



8 



16 





15 



a = 26 b = 4'8' 



2 (5 2) (2 III)" 



abb 



14 



8 



17 



J? 



15 



a = 4'8' b = B'T 



451(2 111) 



abb 



14 



8 . 



18 





15 



a = 4'8' b = 2 6 



45(2111) 



