536 



Ab- 



Sym- 

 metrie- 

 art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Symbol 

 des Systems 



leitungs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



-,11 



a 



15' 



16 



49 



lOxIII 



1357 



a 1'3'5'7' 



a' 2' 4' 6' 8' 



10;^l(8m)i-2' 



a 



15 



16 



50 





1 357 



«_^;^!^'/',&-2468 

 a' 2' 4' 6' 8' 



llzl(8IIl)i-2' 



abb 



15 



16 



51 





13' 5 7' 



a = 1' 3 5' 7 & = 2 4' 6 8' 



18 (xD (2^ III) 



abb 



15 



16 



52 





1 3' 5 7' 



a = 1' 3 5' 7 ö = 2' 4 6' 8 



18 U 3) (2 .Till) 



abb 



15 



16 



53 





13' 5 7' 



o = 24'68' ö = l'35'7 



10;f3(2^III) 



abb 



15 



16 



54 





1 3' 5 7' 



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



8(;^4)(2jrIII) 



abb 



15 



16 



55 





1 3' 5 7' 



a = 2' 4 6' 8 & = 1' 3 5' 7 



7(;.4)(2jrIII) 



abb 



15 



16 



56 





1 3' 5 7' 



a = 2'46'8 & = 24'68' 



18 (/2) (2^ III) 



a a a 

 a' a' a' 



a a a 

 a' a' a' 

 a a a 

 a' a' a' 



abc 

 abe 

 ab c 

 abe 

 ab c 

 ab c 



20 



19 

 19 



12 



V. Hexagonale Syngonie. 



165 III 



Ulla 



a __ 5' 5i' öä' 

 a' 4' 4i' 42' 



VI. Kubische Syngonie. 



a aj a^ 



28 



12 



1 



a % «2 



28 



12 



2 



a a^ 02 



29 



24 



1 



aa^ «2 



29 



24 



2 



a tti a^ 



30 



24 



1 



a «1 «2 



31 



24 



1 



a a^ a^ 



32 



48 



1 



19 III 



llll2 = (l)3 



„ 



llll2 = (l)3 



19;i; III 



1 ljl2 5 5i 52 



= (15')3 



" 



1 Ij 12-5 5i 02 



= (15')3 



195 III 



(18)3 



22 III 



(1 4')3 



22 ;t; III 



(1 4' 6' 8)3 



a = 22' 5i 6' «1 = 2' 52 61' 



(I2 = 2i' 5 62' 

 a = 2i b 62' «1 = 22' 5i 6' 



«2 = 2' 02 61' 

 a = 1' 22 2,' 5 6i 62' 

 % = li' 2 22' 5i 62 6' 

 «2 = I2' 2i 2' 52 6 61' 

 a =1/2 22' 5i 62 6' 

 «1 = h' 2i 2' 02 6 61' 

 «2= 1' 22 2i' 5 61 62' 

 a = 2i' 3i' 4 5 62' 72' 

 % = 22' 32' 4i 5, 6' 7' 

 02 = 2' 3' 42 52 61' 7i' 

 a = 2i' 32 5 62' 7i 8' 

 a, = 22' 3 5i 6' 72 8/ 

 «2 = 2' 3i 52 61' 7 82' 

 n = 1 '222i'323i'4 5 6i62'7i72'8' 

 ai= li'2 22'3 32'4i5i626'727'8,' 

 %= I2'2i2'3i3'42526 6i'7 7i'82' 



14a 1(13 111)4-5- 



(22) (13 III) 

 20 (13 III) 

 20/(13jrIII) 



22(;);l)(137rIII) 



20 5 (13?) III) 



23 (16 III) 



23/(165111) 



Triparalleloedersysteme VI. Ordnung. 



16 III 1 



1 



a^_4^ 

 a' 4i' 



fL — *!_ 



a' 42' 



(26) (IUI), 



(27) (1 III), 



Triparalleloödersysteme VIII. Ordnung. 

 III. Rhombische Syngonie. 



8 



8 



1 



4/ III 





8 



8 



2 







8 



8 



3 







8 



8 



4- 







8 



8 



5 







8 



8 . 



6 







a= 1' 



b = 2 



c = 6 



4/(1 III4) 



a = 5' 



b = 2 



c = 6 



2(/3)(lIIl4) 



a = 2' 



b = 2 



c = 6 



3(/l)(lIIl4) 



a=l' 



b = 5' 



c = 2' 



14(/1)(1III4 



a= 1' 



b = 5' 



c = 6' 



2(/2)(lIIl4) 



a=l' 



& = 6' 



c = 2' 



2(/4)(lIIl4) 



