571 



Ab- 

 leitungs- 

 form 



Sym- 



metrie- 



art 



Sym- 

 metrie- 

 grösse 



Nr. 



Typus 

 I. Ordnung 



Charakteristische Zahlen 



Explicite 

 Symmetrie 



Verbandsymmetrie 



Symbol 

 des Systems 



V. Hexagonale Syngonie. 



al 1 



17 



6 



1 



a 11 



17 



6 



2 



all 



18 



6 



1 



oll 



19 



6 



1 



all 



19 



6 



2 



al 1 



20 



12 



1 



a 1 1 



20 



12 



2 



all 



20 



12 



3 



al 1 



20 



12 



4 



all 



20 



12 



5 



al 1 



20 



12 



6 



al 1 



21 



6 



1 



al 1 



22 



12 



1 1 



al 1 



22 



12 



2 1 



al 1 



22 



12 



3 i 



all 



23 



6 



1 I 



all 



24 



12 



1 



al 1 



24 



12 



2 ' 



al 1 



24 



12 



3 



all 



25 



12 



1 



all 



25 



12 



2 ! 



all 



25 



12 



3 



all 



26 



12 



1 



all 



26 



12 



2 



all 



26 



12 



3 



al 1 



26 



12 



4 



all 



26 



12 



5 



all 



26 



12 



6 



al 1 



27 



24 



1 1 



all 



27 



24 



2 



all 



27 



24 



3 



al 1 



27 



24 



4 



nl 1 



27 



24 



5 



a 1 1 



27 



24 



6 



"" 



27 



24 



7 



12?? IV 

 \2(p'lY 

 12a IV 

 14 IV 

 15 IV 

 14 a IV 



15 a IV 



17 IV 

 17^ IV 



12^' IV 

 17/ IV 



18 IV 



UjtIV 



lÖJiIV 



18/ IV 



159 



159 



159 



159 



1 59 



1 4 589 12 



13' 5 7' 9 11' 



1 2' 5 6' 9 10' 



1 2 5 6 9 10 



13' 5 7' 9 11' 



1 4' 5 8' 9 12' 



159 



1357911 



1458912 



1 2 5 6 9 10 



159 



13' 5 7' 9 11' 



1 357911 



1 1' 5 5' 9 9' 



12' 5 6' 9 10' 



1 4' 5 8' 9 12' 



1357911 



1 2' 5 6' 9 10' 



1 2 5 6 9 10 



1 1' 5 5' 9 9' 



1 4' 5 8' 9 12' 



14589 12 



1 1' 5 5' 9 9' 



12' 3' 4 5 6' 7' 



8 9 10' 11' 12 



123'4'567'8' 



9 10 11' 12' 



12345678 



9 10 11 12 



11'33'55'77' 



99' 11 11' 



12'34'56'78' 



9 10' 11 



11'22'55'66' 



9 9' 10 10' 



11'44'55'88' 



99' 12 12' 



^48 12 



26 10 



3' 7' 11' 

 : 2' 6' 10' 

 : 4' 8' 12' 

 ■■ 2' 8' 6' 7' 10' 11' 



2' 4 6' 8 10' 12 



3' 4 7' 8 11' 12 



3' 4' 7' 8' 11' 12' 



2 4' 6 8' 10 12' 



2 3' 6 7' 10 11' 



3711 



2468 10 12 



2 367 10 11 



3 47 8 1112 

 : 1' 5' 9' 



1' 3 5' 7 9' 11 

 ■■ 1' 3' 5' 7' 9' 11' 



3 3' 7 7' 11 11' 



3 4' 7 8' 11 12' 



2' 3 6' 7 10' 11 

 ■- 2' 4' 6' 8' 10' 12' 

 : 1' 2 5' 6 9' 10 

 : 1' 2' 5' 6' 9' 10' 



2 2' 6 6' 10 10' 

 :1' 4 5' 8 9' 12 

 : 1' 4' 5' 8' 9' 12' 

 : 4 4' 8 8' 12 12' 

 : 1' 2 3 4' 5' 6 7 8' 9' 10 



11 12' 

 :1' 2' 3 4 5' 6' 7 8 9' 10' 



11 12 



:1' 2' 3' 4' 5' 6' 7' 8' 9' 



10' 11' 12' 

 : 2 2' 4 4' 6 6' 8 8' 10 10' 



12 12' 



:1' 2 3' 4 5' 6 7' 8 9' 10 



11' 12 

 : 3 3' 4 4' 7 7' 8 8' 11 11' 



12 12' 

 : 2 2' 3 3' 6 6' 7 7' 10 10' 



11 11' 



12(?>l(12IV)s 

 12 ?>' 1 (12 lV)s 

 12a{12IV)s 

 14 (12 IV)s 

 15(12IV)s 

 14a(12?'IV)s 

 14al(12aIV)s 

 14al(141V)s 

 15a(12<pIV)s 

 15al (l2aIV)s 

 15al(15IV)s 

 (28) (12 lV)s 

 17<?'l(17IV)s 

 28{<}>l){l2cplY)^ 

 2S{(p2)(l2(p'lV)^ 

 12jr(12IV)s 

 28(/l)(12aIV)s 

 17/(17IV)s 

 28(zl){127rlV)s 

 (33) (14 IV)s 

 (33) 15 IV)s 

 18 (17 IV)s 

 14jrl(14IV)' 

 14jr(12(?^'IV)s 

 14.-rl (12jrIV)s 

 lÖJrl (15IV)s 

 15jr(12<?'IV)s 

 15.T(12;rIV)s 

 33(/l)(14aIV)s 



33(/2)(l5aIV)s 



18/(17<pIV)s 



18/l(17/IV)s 



18/l(18IV)s 



33(/2)(14;rIV)' 



33(/1)(15jiIV)s 



Tetraparalleloedersysteme III. Ordnung. 



-11 

 a 



a 

 h V 



a a a' 

 a' a' a 

 a a a' 

 a' a' a 



16 



3 



1 



16 



3 



2 



16 



3 



3 



16 



3 



4 



16 



3 



5 



12 IV 



a 



_9 



u' 5 



a 5 



^~9 

 ö__5 



a _9 

 a' 5 

 a 5 

 ä'~9 



(10) (1 IV),. 



(ii){iiv); 



12 (1 INY 

 13(1 IV), 



13 (l IV)^ 



73' 



