556 



Ab- 



leituugs- 



form 



Sym- 

 metrie- 

 art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Explicite 

 Symmetrie 



Verbandsymmetrie 



Symbol 

 des Systems 



a a a 

 a a a 

 a a a 

 laa 

 aaa 

 laa 

 laa 

 laa 

 aaa 

 aaa 

 aaa 

 laa 

 laa 

 laa 

 aaa 

 aaa 

 aaa 

 laa 

 laa 

 laa 

 laa 

 laa 

 laa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 laa 

 laa 

 laa 

 laa 

 laa 

 Ina 

 laa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 



10 



8 



1 



10 



8 



2 



10 



8 



3 



11 



8 



1 



11 



8 



1 



12 



8 



1 



12 



8 



2 



12 



8 



3 



12 



8 



1 



■ 12 



8 



2 



12 



8 



3 



13 



8 



1 



13 



8 



2 



13 



8 



3 



13 



8 



1 



13 



8 



2 



13 



8 



3 



14 



8 



1 



14 



8 



2 



14 



8 



3 



14 



8 



4 



14 



8 



5 



14 



8 



6 



14 



8 



1 



14 



8 



2 



14 



8 



3 



14 



8 



4 



14 



8 



5 



14 



8 



6 



15 



16 



1 



15 



16 



2 



15 



16 



3 



15 



16 



4 



15 



16 



5 



15 



16 



6 



15 



16 



7 



15 



16 



1 



15 



16 



2 



15 



16 



3 



15 



16 



4 



15 



16 



5 



15 



16 



6 



15 



16 



7 



99p VII 



3^ VI 

 3jrVII 

 2(pYI 



9;^ VII 



ii'vi 



11 VII 

 IdYl 

 Qd\l 

 6 .5 VII 

 7 .5 VII 

 11/ VI 



11;!; VII 



1256 



1458 



1357 

 15 

 15 



1 1' 5 5' 



1 3' 5 7' 



1357 



11' 5 5' 



13' 5 7' 



1357 



1 2' 5 6' 



1 4' 5 8' 



1357 



1 2' 5 6' 



1 4' 5 8' 



1357 



1 2' 5 6' 



1458 



13' 5 7' 



1 4' 5 8' 



1256 



13' 5 7' 



1 2' 5 6' 



1458 



13' 5 7' 



1 4' 5 8' 



1256 



1 3' 5 7' 

 1 1'2 2'5 5'6 6' 

 1 1'4 4'5 5'8 8' 

 12345678 

 1 1'3 3'5 5'7 7' 

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

 12'3'4 5 6'7'8 

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

 1 1'2 2'5 5'6 6' 

 1 1'4 4'5 5'8 8' 

 12345678 

 1 1'3 3'5 5'7 7' 

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

 12'3'4 5 6'7'8 

 12 3'4'o6 7'8' 



a = 3 

 a = 2 

 a = 2 

 a= 3' 

 a = 3' 

 a = 3 

 0=1' 

 a = 1' 

 a= 3 

 a= 1' 

 a= 1' 

 a= 3 

 a = 2' 

 a = 2' 

 a = 3 

 a = 2' 

 a = 2' 

 a = 3' 

 a = 2' 

 a = 2' 

 fl = 2 

 a = 3' 

 rt = 2 

 a = 3' 

 a = 2' 

 a = 2' 

 a = 2 

 a = 3' 

 a = 2 

 a = 3 

 « = 2 

 a= 1' 

 a = 2 

 a=l' 

 a= 1' 

 a= 1' 

 a = 3 

 a = 2 

 a = 1' 

 a = 2 

 a= 1' 

 a = 1' 

 a= 1' 



478 

 367 

 468 



7' 



7' 

 3' 7 7' 



3 5' 7 



3' 5' 7' 

 3' 7 7' 



3 5' 7 



3' 5' 7' 

 4' 7 8' 



3 6' 7 



4' 6' 8' 

 4' 7 8' 



3 6' 7 

 4' 6' 8' 



4 7' 8 

 3' 6' 7' 

 4 6' 8 



3' 6 7' 

 4' 7' 8' 

 4' 6 8' 

 4 7' 8 

 3' 6' 7' 

 4 6' 8 

 3' 6 7' 

 4' 7' 8' 

 4' 6 8' 



3' 4 4' 7 7' 8 8' 

 ü' 3 3' 6 6' 7 7' 

 2' 3' 4' 5' 6' 7' 1 

 2' 4 4' 6 6' 8 8' 

 2 3' 4 5' 6 7' 8 

 2 3 4' 5' 6 7 8' 

 2' 3 4 5' 6' 7 8 

 3' 4 4' 7 7' 8 8' 

 2' 3 3' 6 6' 7 7' 

 2' 3' 4' 5' 6' 7' ! 

 2' 4 4' 6 6' 8 8' 

 2 3' 4 5' 6 7' 8 

 2 3 4' 5' 6 7 8' 

 2' 3 4 5' 6' 7 8 



6{(p\){i(p'Yliy/ 

 6(9^3)(3 93"VII).'? 

 8 9p 3 (9 VII)«/ 

 2.-r(3VI)s 

 2.'r(3VII)Ä' 



6(;i;2)(3.-rVI)s 

 8;j:1(9VI)« 

 6^1) (3z VII).? 

 6(;t;2)(3.TVII)y 

 8-/1 {9 VII)? 

 (18)(7VI)s 

 (8) (6 VI)s 



(7) (9 VI)s 



(8) (6 VII)'/ 

 (18)(7VII).5' 

 (7) (9 VII).'/ 

 5.5 3(7VI)s 

 5 3(3r/)'VI)s 

 5 53(3jrVl)s 

 4^1(6VI)s 

 2{ö\)(3(p"Yl)^ 

 2((52)(3jrVI)s 



4 ^ 1 (6 Yll)!/ 



2(<31){3<)9"VII)? 



2 ((5 2) (3 JT VII)* 



5<5 3(7VII)£' 



bdiSfp'YlTjff 



5d3(3jiYll)ff 



18(;^1)7/VI)5 



8(zI)(6zVI)« 



7 (/ 2) (9 9> VI)s 



7(;^3)(9/VI)s 



10;/3(11 VI)s 



18(^4) (7 5 VI)« 



8U3)(6.5VI)s 



8(;^1)(6;.VII).(/ 



18(;^l){7xVII).? 



7 ix 2) (9 <p YUyj 



10/3(11 VII)'/ 



8 ix 3) (6 d Yiiyj 



18(/4)(7ÖVII).'/ 



aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 aaa 

 a a a 

 aaa 

 aaa 



17 



6 





17 



6 





18 



6 





18 



6 





19 



6 





19 



6 





20 



12 





20 



12 



2 



20 



12 



3 



20 



12 



1. 



20 



12 



2 



20 



12 



3 



V. Hexagonale Syngonie. 



13(pYl 

 13 9^ VII 

 13aVI 

 13 a VII 

 16 VI 

 16 VII 

 16 a VI 



16 d VII 



11112 



a = 8 81 83 



11112 



a = 8 8, 82 



Ulla 



a = 5' 5i' 52- 



11112 



a = 5' 5i' 52' 



11112 



a = 4' 4,' 42' 



11112 



a = 4' 4i' 4o' 



(18)3 



a=(4'5')3 



(15')3 



= (6' 8)3 



(14')3 



a = (4' 8)3 



(18)3 



a = (4' 5')3 



(15')3 



a = (5' 8)3 



(14')3 



a = (4' 8)3 



1395 1(13 VI)" 

 13 9Jl(13VII).0' 

 13 a (13 VI)« 

 13a(13VII)? 

 16 (13 VI)« 

 16 (13 VII)» 

 16a(139>VI)« 

 16al (16 VI)« 

 16a 1 (13a VI)« 

 16a (13 9? VII)-/ 

 16 a 1(16 VII)-'/ 

 16 a 1(13 a VII)'/ 



