572 



Ab- 



Sym- 



itungs- 



metrie- 



form 



art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Explicite 

 Symmetrie 



Verbandsymmetrie 



Symbol 

 des Systems 



b'b 

 bj^ 

 b'b 



-, 1 1 



bb: 

 b'b 

 b_b^ 

 b'b 



-11 

 a 



a 

 b__b^ 



b'b 



17" 



19 



21 



21 



23 



24 



25 



25 



26 



6 



6 



6 



6 



6 



12 



12 



12 



12 



12?>IV 



18 



15 IV 



18' 



17 IV 



17 



17 IV 



17 



12jiIV 



11' 



17/ IV 



11' 7 7' 



18 IV 



1 2' 7 8' 



18 IV 



1 2' 7 8' 



15^ IV 



1 1' 8 8' 



ö^^5 

 b' 4 

 &^_5 

 b'~ A 

 «^_3 

 ct/~ 5 

 a _ 5 

 a^'^S 



b'~9 



b_^5 



b' 



a 



a' 



a 



a' 



b^ 



b' 



12 

 9 



12' 



'9 



9 



11 



n. 



9 

 5^ 

 9' 

 5' 11 11' 



3 3' 



3 4' 



9 9' 

 9 10' 



5 6' 

 5 6' 



11 12' 

 11 12' 



3 4' 

 5 5' 



9 10' 

 12 12' 



4 4' 9 9' 



129>'(l;i;'IV)'^ 

 14 (4 IV'K 



(29) (3 IV),'. 



(30) (3 lYfi 

 l2.-r{lxlY)U 

 28(zl){2xlY)U 



(34) (5 IV)^. 



(35) (5 IV)f 

 Un{3cplY)l-^ 



Tetraparalleloeder IV. Ordnung. 

 IL Monokline Syngonie. 



abl 

 abl 

 abl 

 abl 

 abl 

 all 

 Ibc 

 übe 

 ah c 

 ah c 



"ll 

 a 



^&1 

 a 



b 



b 



az- a 



b 



ab 1 



abl 



abl 



ah 1 



abl 



ab 1 



^11 



5 



4 



1 



5 



4 



2 



5 



4 



3 



5 



4 



4 



5 



4 



5 



5 



4 



6 



5 



4 



7 



5 



4 



8 



5 



4 



9 



5 



4 



10 



5 



4 



11 



5 



4 



12 



5 



4 



13 



5 



4 



14 



5 



4 



15 



5 



4 



16 



5 



4 



17 



5 



4 



18 



5 



4 



19 



5 



4 



20 







4 



21 



5 



4 



22. 



5 



4 



23 



2xIV 



3/ IV 



1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 

 1 



a = 7' 

 a = T 

 a = 7 

 a = 7 

 a=l' 

 a=l' 

 &=7' 

 a = 7' 

 a = 7 

 « = 1' 



5 = 7 

 5 = 1' 

 5 = 7' 

 5 = 1' 

 5 = 7' 

 5 = 7 

 c = 7 



5 = 7' c = 7 



6 = 1' c = 7 

 6 = 1' c = 7 



2zl(lIV2)Ä 



1(;^2)(1IV2)'' 



1(;.2)(1IV2)''- 



1(/2)(1IV2)/' 



l(;fl)(llV2)'' 



2/(1 IVo)'' 



2xl{l\Y^Y 



3/1(11^2) 



%X1{\\Y^' 



SzdIVa) 



1 



a 7' 





1 (Z 1) (1 IV2)» 



1 



a _7' 

 a'~ 1' 



5 = 7 



SzdlV^)" 



1 



b T 

 b'~7 





2zl(lIV2)'' 



1 



h T 

 h'~7 



a = l' 



3;cdIV2)''- 



1 



b T 

 &'~7 



c = l' 



2/l(lIVa)«' 



1 



h __T 

 V ~ 7 



« = !'■ 



3 x (1 IV2) 



1 



1 

 1 

 1 

 1 

 1 



a = 7' 

 a = 7' 

 a = 2' 

 a = 2' 

 a = 8 

 rt = 8 



5 = 2' 

 5 = 8 



5 = 7' 



6 = 8 

 6 = 7' 

 6 = 2' 



1(;/2)(1IV3)Ä 

 l(z2)dIV3)''' 

 2zldIV3)'' 

 2;^1(1IV3)A' 

 1 (;. 2) (1 IV3)*' 

 l(^2)(lIV3)''' 



1 



a 7' 

 ä'~ 2' 





3zUllV3)^V 



