537 



Ab- 



Sym- 



metrie- 



art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristisclie Zahlen 



Symbol 

 des Systems 



leitungs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



ahc 



8 



8 



7 



4x111 



1 



a=l' b = 5 c = 6' 



3{x2)(llIU 



ah c 



8 



8 



8 



„ 



1 



a=l'& = 5 c = 2' 



2(;^4)(lin4)' 



abc 



8 



8 



9 



„ 



1 



a=l' b = 2' c = 6' 



4^1(11114) 



ahc 



8 



8 



10 



„ 



1 



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



2(z6)(llll4) 



ah c 



8 



8 



11 



,, 



1 



a = 5' & = 5 c = 2' 



2(z5)(lIIl4) 



ah c 



8 



8 



12 



,, 



1 



a=5' & = 5 c^6' 



3U4)(lIII.i) 



ahc 



8 



8 



13 



„ 



1 



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



4^3(1111,) 



ahc 



8 



8 



14 



„ 



1 



rt=l' ft = 6 c = 2 



2U1)(1I1I4) 



ahc 



8 



8 



15 



,, 



1 



a=:l'& = 6 c = 5' 



14(;;l)(llll4)' 



ah c 



8 



8 



16 



„ 



1 



a=l' b = Q e = 2' 



MUDdllU" 



ah c 



8 



8 



17 



„ 



1 



o= V b = G c = 5 



2(zi){ini4)' 



abc 



8 



8 



18 



,, 



1 



a=5'& = 6 c = l' 



2(/5)(llll4)' 



abc 



8 



8 



19 



„ 



1 



a = 5'& = 6 c = 2 



4;^ 2(11114) 



abc 



8 



8 



20 



„ 



1 



a = 5' h = (i c = 5 



3(/3)(lIll4) 



ahc 



8 



8 



21 



„ 



1 



rt = 5'& = 6 c = 6' 



3(z4)(lIIl4)' 



ahc 



8 



8 



22 



„ 



1 



« = 5' b = l' c = 2' 



14(z2)(lIIl4) 



abc 



8 



8 



23 



„ 



1 



a=b' h=l' c = 6' 



2{z6){llll4)' 



ahc 



8 



8 



24 



„ 



1 



a=6 b= l' c = 2 



14(;.2){1III4)' 



ahc 



8 



8 



25 



») 



1 



a = 2' h = 6 c = 2 



3(;f3)(llll4)" 



ahc 



8 



8 



26 



,, 



1 



ft=5 h = Q c=l' 



14U2)(lin4)" 



abc 



8 



8 



27 



,, 



1 



a = 2' h = Q c = 1' 



2(z5)(lin4)" 



abc 



8 



8 



28 



„ 



1 



a = 5 b = 2' c = 1' 



2(;ffi)(llll4)" 



abc 



8 



8 



29 



„ 



1 



a = Q' h = 2' e=l' 



3{z3)(lIIl4)' 



abc 



8 



8 



30 



„ 



1 



a = 2' b = 5 e=l' 



3(z4){lll]4)" 



abc 



8 



8 



31 



„ 



1 



a=& h = b c=l' 



4^2(11114)' 



ahc 



8 



8 



32 



„ 



1 



a = 2' /; = 6' c = l' 



2{xb){\Uh)"' 



abc 



8 



8 



33 



„ 



1 



a=5 & = 6' c=l' 



2(;.5)(1III4F 



a 



-bl 



a 



8 



8 



34 



" 



1 



" 2' 



-7=i^ b = 2 

 a 6 



3(;(2)(1III4W 



-b 1 

 a 



8 



8 



35 



>. 



1 



« 2' ^ 

 -, = r; ^^ = 6 

 a 6 



3 (;f 3) (11114)^,6- 



« , 













a 2' 





-.bc 

 a 



8 



8 



36 



" 



1 



- = ^7 ?' = 2 c = 5 

 a 6 



5;^1(1III4W 



—,be 

 a 



8 



8 



37 



" 



1 



^=1 = 6 = 5 

 rt 6 



5/3(lIIl4)2,g< 



~bc 

 a 



8 



8 



38 



■ 



1 



a 2' , 



^ = ^ & = 2 = 2 



4 te 2) (1 1114)2-6' 



" 7 



—,hc 

 a 



8 



8 



39 



,, 



1 



J=^&=2 0=6 

 a 6 



5 (;^1) (11114)2-6' 



0- , 













a 2' 





-bc 

 a 



8 



8 



40 



.. 



1 



- = ^ ö = 6 = 2 

 a 6 



5 iz 2) (l IIl4)2<6' 



-b 1 

 a 



8 



8 



41 





1 



« 5' „ 

 - = 77 & = 2 

 a 1 



2(;^3)(lIIl4)^5, 



'-,bl 

 a 



8 



8 



42 



,, 



1 



rt 5' , 



-, = 77 & = 6 



a 1 



2 (;^ 2) (11114)^5, 



« , 













a 5' 





-,bc 

 a 



8 



8 



43 



" 



1 



- = 77 = 2 = 5 



a 1 



4 (;.!) (11114)1,5, 



%bc 

 a 



8 



8 



44 



„ 



I 



« 5' „ 



-; = r-; & = 6 = 5 



«' 1' 



4 (;f 2) (11114)1,5. 



« , 













a 5' , 





— hc 

 a 



8 



8 



45 



" 



1 



- = -7 ^^ = 2 = 2 

 a' 1' 



4 (;^1) (11114)1 ,5. 



« , 













a 5' 





-he 

 a 



8 



8 



46 



" 



1 



- = ^ ?^ = 2 = 6 

 a 1 



ezdiiWi-s- 



a , 



—,bc 



a 



8 



8 



47 



" 



1 



«, = ^ ö = 6 = 2 

 a 1 



ezKiiiUi-y 



Abb. d. II. Gl. d. k. Ak. d. Wiss. XX. Bd. II. Abth. 



69 



