542 



Ab- 



Sym- 

 metrie- 

 art 



Syra- 

 metrie- 

 gi-össe 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Symbol 

 des Systems 



leituugs- 

 form 



Explicite 

 Symmetrie 



Verbandsymmetrie 



ab c 



15 



16 



24 



10;i:III 



14' 



n = l'4 & = 36' c = 2'7 



7{;;3)(411I) 



ab c 



15 



16 



25 



,, 



14' 



a = 5'8 = 36' c = 2'7 



7te4)(4IIl) 



ab c 



15 



16 



26 



,, 



14' 



a = 1'4 ö = 3'6 c = 2 7' 



18 U3) (4 III) 



ab c 



15 



16 



27 



,j 



14' 



a = 5'8 ö = 3'6 c = 27' 



8^4) (4 III) 



ab c 



15 



16 



28 



,, 



1 1' 



a = 4 4' & = 3 3' c = 7 7' 



7(z3)(l/III) 



ab c 



15 



16 



29 



>i 



1 1' 



rt = 8 8' & = 3 3' c = 7 7' 



10z 1 (Ulli) 



abc 



15 



16 



30 



)> 



1 1' 



a = 4 4' & = 2 2' c = G6' 



8Ui)(i/ni) 



abc 



15 



16 



31 





1 1' 



a = 44' & = 66' c = 2 2' 



18 (z 3) (1/ III) 



^b'c' 



15 



16 



32 



)) 



1 1' 



b 3 3'c 7 7' 

 b'~ 2 2' c' ~ 6 6' 



lixDHxmls 



b c 

 b c 



15 



16 



33 



)) 



1 1' 



^_o8'^ -33'c _77' 

 ""-^^ b'-22'c'-66' 



iizi(izin),3 



abc 



15 



16 



34 



j, 



18 



a == 1'8' fc = 23 c = 67 



lox(u'iii) 



abc 



15 



16 



35 



jj 



18 



a=r4'5' & = 23 c = 67 



7 (z 2) dz' III) 



ahc 



15 



16 



36 



j, 



18 



a = 1'8' b = 2'3' c = 6'7' 



8(z2){lz'III) 



abc 



15 



16 



37 



j, 



18 



a = 4'5' b = 2'3' c = 6'7' 



8 (z 3) dz' III) 



abc 



15 



16 



38 



,, 



14 



a = 1'4' 6 = 36 c = 27 



7(zi)(iz'ni) 



abc 



15 



16 



39 



jj 



14 



a = 5'8' & = 36 c = 27 



10z 2 dz' III) 



abc 



15 



16 



40 



jj 



14 



a = 1'4' b = 3'6' c = 2'7' 



i8(zi)dz'in) 



abc 



15 



16 



41 



jj 



14 



a = 5'8' b = 3'6' c = 2'7' 



«=f8', fe = 36 c = 27 

 a 14 



18 (z 2) dz' III) 



—,bc 

 a 



15 



16 



42 



j) 



14 



iizi(iz'ni)i.5, 



a , 

 — & c 

 a 



15 



16 



43 



>» 



18 



«, = ;j; Z, = 23 c = 67 

 a' 4'5' 



iiz(iz'ni)i-4' 



4- 



V c' 



15 



16 



44 



„ 



18 



b 23 c 67 

 b' ~ 2'3' e' ~ 6'7' 



7 (z 2) dz' 111)^3, 



b c 

 b' c' 



15 



16 



45 



)) 



18 



-,_, h 23 c 6 7 



""-^^ b' - 2'3' c - er 



11z dz' 111)3 3' 



VI. Kubische Syngonie. 



a «1 «2 

 a tti «2 

 a rtj 02 

 a «1 a^i 

 a «1 «2 



a a^ a^ 



a ai 02 



29 



24 



1 



29 



24 



2 



30 



24 



1 



31 



24 



1 



32 



24 



1 



32 



24 



2 



32 



24 



3 



19z in 



19(5111 



22 m 



2 2z III 



II1I2 

 II1I2 

 II1I2 

 II1I2 



(15')3 



(18)3 



(U')3 



a= l'22 6i a= li'2 62 



02= l2'2i6 



a=l2'2i6 «1=1' 22 61 



02=1,' 2 62 



a = 3i' 4 72' «1 = 82' 4i 7' 

 a^ = 3' 42 7i' 



a = 32 7i 8' «1 = 3 72 81' 

 (I2 = 3i 7 82 



a = 82 3i' 4 7i 72' 8' 



«1 = 3 32' 4i 72 7' 81' 

 «2 = 3i 3' 42 7 7i' 82' 



a = 1' 22 32 61 7i 8' 



«1 = li' 2 3 62 7, 81' 

 «2 = I2' 2i 3i 6 7 82' 



a = 1' 22 3i' 4 6,72' 



Ol =li' 2 82' 4, 627' 

 «2 = I2' 2i 3' 42 6 7i' 



19 z (13 III) 

 25 (zD (13 111) 

 19(51(13111) 

 22(13111) 

 22z l (13a III) 



22 z (13 9> III) 



9 (zl) (16 III) 



