528 



Ab- 



Sym- 

 metrie- 

 art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Symbol 

 des Systems 



leitungs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



all 



15. 



16 



7 



10;tIII 



12345678 



a = 1' 2' 3' 4' 5' 6' T 8' 



10 ;i: (89^111)8 



laa 



15 



16 



8 



jj 



12345678 



a = l'2'3'4'5'6'7'8' 



10^(89^111)'= 



aaa 



15 



16 



9 



j, 



12345678 



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



UxiScpUl) 



all 



15 



16 



10 



,j 



11'33'55'77' 



rt = 22'4 4'6 6'8 8' 



lOzKS;^!!!)' 



laa 



15 



16 



11 



jj 



11'33'55'77' 



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



7(xl)(8xIlIK 



aaa 



15 



16 



12 



,, 



11'33'55'77' 



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



ll;(l(8;tlll) 



all 



15 



16 



13 



,j 



12'34'56'78' 



rt= 1'23'45'67'8 



10/l{10III)s 



laa 



15 



16 



14 



,j 



12'34'56'78' 



a = l'23'45'67'8 



10;t;2(10IIIK 



aaa 



15 



16 



15 



jj 



12'34'56'78' 



a= 1'23'45'67'8 



ll;i; 1(10 III) 



all 



• 15 



16 



16 



,j 



12'3'456'7'8 



a = 1'234'5'678' 



8(/2)(4.5IlI)s 



laa 



15 



16 



17 





12'3'456'7'8 



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



10/2(4(5111)« 



aaa 



15 



16 



18 





12'3'456'7'8 



rt=l'234'5'678' 



11/1(45111) 



all 



15 



16 



19 



,j 



123'4'567'8' 



a=l'2'345'6'78 



8 (/]) (5(5111)8 



laa 



15 



16 



20 



j, 



123'4'567'8' 



a=l'2'345'6'78 



10/2(5(51II)<^ 



aaa 



15 



16 



21 



" 



123'4'567'8' 



a= 1'2'345'6'78 



11/1(55111) 



aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 



aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 



V. Hexagonale Syngonie. 



17 



6 



1 



18 



6 



1 



19 



6 



1 



20 



12 



1 



20 



12 



2 



20 



12 



3 



139)111 

 13 a 111 

 16111 

 16 a III 

 16 a III 

 16 a III 



Ulis 



II1I2 



II1I2 



1 Ij 1^8 81 82 



iiii24;4,;42; 



1 ll lib'bi'b'i 



a = 8 81 82 



a ^ 5 5i 02 



a = 4' 4i' 42' 



a = 4' 4,' 42' 5' 5i' 52' 



a = 5' 5i' 62' 8 8i 82 



a = 4' 4i' 42' 8 81 82 



VI. Kubische Syngonie. 



29 



24 



1 



30 



24 



1 



31 



24 



1 



32 



48 



1 



32 



48 



2 



32 



48 



3 



19/ III 

 19.5 111 

 22 III 

 22/111 

 22/ 111 

 22/ 111 



(1 2' 5 6')3 



(1 2' 5 6')3 



(12' 5 6% 



(11'22'55'66')3 



(12'3'456'7'8)3 



(12'34'56'78')3 



a = (1' 2 5' 6)3 



rt = (3' 4 7' 8)3 



a = (3 4' 7 8')3 



a = (3 3' 4 4' 7 7' 8 8% 



a = (1' 2 3 4' 5' 6 7 8% 



a = (1' 2 3' 4 5' 6 7' 8)3 



aaa 

 a' a' a' 



16 



3 



1 



aaa 

 a' a' a' 



16 



3 



2 



aaa 

 a' a' a' 



19 



6 



1 



aaa 

 a' a' a' 



19 



6 



2 



Triparalleloödersysteme III. Ordnung. 

 V. Hexagonale Syngonie. 



13 III 



13 III 1 



16 III 14' 



16 III 14' 



h 



ll 



Li 



12 



laV 



li4i' 

 liV 



l2 4o' 



IS?' 1(18111) 

 13a (13 III) 

 16(13111) 

 16a (1399 111) 

 16a 1(16 III) 

 16a 1 (13a 111) 



21/1(19111) 

 2151 (19111) 

 (9) (19 III) 

 24/1(19/111) 

 24/(195111) 

 24/1(22111) 



(10) (IUI),- 

 (iDdllDz 



(12) (3 III)r 



(13) (3 III); 



lab 



5 



4 



1 



lab 



5 



4 



2 



lab 



5 



4 



3 



abl 



5 



4 



4 



abl 



6 



4 



5 



abl 



5 



4 



6 



Triparalleloödersysteme IV. Ordnung. 

 IL Monokline Syngonie. 



2/ III 





a = b' b = 5 



2/1(1 111,)'' 





a = b' b = l' 



2/ 1 (1 III2)''' 





a = b b = l' 



2/ 1 (1 III2)«" 





a^=b' b=:5 



2/ 1 (1 UhK' 





a = b' b = l' 



1(/2)(1III2)« 





a = 5 h = b' 



l(/2)(llll2)«' 



