[105] 



Untersuchungen über gleichflächige Polyeder. 



147 



Art 



Name 



Typns 



D 



Art der Ecken 



6 



n 



(1 = 2). (3 = 5). (4 = 6). (7 = 11). (9 = 13). (16 = 17) 

 (1 = 2). (3 = 5). (7 = 11). (8 = 12). (9 = 13). (10 = 21)! 

 (1 = 2). (3 = 5). (7 = 11). (8 = 12). (9 = 13). (11 = 15) 



I,i(^7)) 



I,g 

 11, i («7) 



A 



X 



X 



62, 61, 3i 

 83,83, 43; 64,64, 3-,; (4,e4,), 



7 



n 

 n 



» 



(1 = 9). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (9 = 13). 



(10 = 21)! 

 (1 = 2). (3 = 5). (1 = 6). (7 = 11). (8 = 12). (9 = 13). 



(11 = 15) 

 (1 = 2). (3 = 5). (4 = 6). (7 = 11). (S = 12). (9 = 13). 



(16 = 17) 

 (1 = 2). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (11 = 15). 



(16 = 17) 

 (1 = 2). (3 = 5). (4 = 6). (7 = 11). (9 = 13). (10 = 21). 



(16 = 17)! 



(1 = 2). (3 = 5). (7 = 11). (8 = 12). (9 = 13). (10 = 21). 



(11 = 15)! 



I,g 

 III,b (a7) 

 11,1(^7) 

 II, n (7) 

 ll,m{ßr) 

 II, k («7) 



A 



43; 64,64; 4i,4„ (4, =4,)» 



83, 83; 3i 



43; 3i; 4i, 4| 



83,83; 6.>, 62, (3i|3i)„; 43,43 



85,85; 3,; (4, =4|)„ 



83,83; 64,64, 3i; (4ih4,)„ 



8 



r 



(1 = 2). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (9 = 13). 



a0 = 21). (11 = 15)! 

 (1 = 2). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (9 = 13). 



(10 = 21). (16 = 17)! 

 (1 = 2). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (9 = 13). 



(14 = 15). (16 = 17) 



U,k(«7) 



n,mißr) 



II, n (7) 



II X. 



eTöi, 3i; (47^i)„ 



85,85,43;64,64,3i;4„4i,(4i=4i)„ 



(3,|3,)„ 



9 



(1 = 2). (3 = 5). (4 = 6). (7 = 11). (8 = 12). (9 = 13). 

 (10 = 21). (14 = 15). (16 = 17)! 



III, c (7) 





(3i|3,)„; (4^)„ 



Es existieren demnach: für w > 2: I8 ganzgeschl. u. 6 halbgeschl. konvexe Polyeder, 



, m < 2: 18 „ „6 „ „ „ , 



rt W^ = ti: 10 y, M^l „ n M* 



Konvexe Begrenzungsfläche besitzen von ihnen: 



für m>2: 3(A) + 3(n), 

 „ m<2:3(A) + 3(D), 

 „ m = 2: 4 (A) + 4 (Q) + 2 (||) + 1 (^9. 



Die Dreiecke sind alle gleichschenklig, die konvexen Vierecke sind 

 Deltoide bezw. Trapeze. 



„i'f" bedeutet ein Rechteck, dessen Kanten das Unendlichweite 

 enthalten. — 



Nova Acta XCIII. Nr. 2. 



19 



