18 ANALYTICAL TREATMENT OF THE POLTTOPES REGULARLY 



"V'3 ^24 [ 5V/2 > V % • V/ - 2 > V ' 3 ] 64 



[ 4V/2 , 2 V .0 , 2\ 2 , 2V 7 2] 64 



[ 3V 2 , 3V/2 , 3\ '2 , V2] 64 



192 



* 2 e 8 ^ 4 [2 -f 5\/2 , 2 -J- 2V/2 , \/2 , \/2] 192 



[2 + 4\ 2 . 2 -f 2Y 2 , 2V / 2 , 2V / 2] 192 



[2 + av 2 . ~ + 3V2 > 3V 2 . V2] 192 



576 



c^e 2 e 3 C 24 [4 + 5V2 ,2+ V/2 , 2+ \/2 , 1/2] 192 



[4 ^- 4V 2 , 2 + 21 2 , 2 -f 2V2 , 2V'2] 1 92 



[4 -j- 8V2 , 2 4- 8V2 , 2 4- SV2 , v 2] 192 



576 



e 1 e 2 e s C ii [0 + 5V2 , 4 -f V% , 2 + V/2, V2] 384 



[6 + 4V/2 , 4 4- 2V 2.2 + 2V'2 , 2V'2] 384 



[6 4" 3N/2 , 4 4- 3V 2,24- 3V 2 » v/2 ] 384 



1152 



E. 77/r characteristic numbers of the C &00 -famify. 



I 15. Forms <?j 6' 600 , «?2 C 600 , e 3 6g 00 . The number of vertices 

 is consecutively 2/;, 3/, 4,-, viz. 1440, 3600, 2400. After 

 this we consider the limiting bodies (000 tT , 120 I for e x 6' G00 ; 

 600 CO, 720 P h , 120 /£> for e 2 C 6(n ; 000 7', 1200 J J :i , 720 P 5 , 

 120 i) for e 3 6' 600 ) and obtain for limiting bodies and faces 720, 

 3600 for e x Q )0 ; 1440, 8010 for e 2 C eoo ; 2640, 7440 for e 3 C 600 . 

 This gives 



C 600 ( 120 , 720 , 1200 . 600) ; 



e 1 C m) (1440 , 4320 , 3600 , 720) ; 



e.,C cm (3600 , 10800 , 8640 , 1440); 



e 3 6 T 600 (2400 , 7200 , 7440 , 2640) . 



146. Forms e x e 2 C 60? , e 1 e H C 600 , e 2 e ;i C 600 , e x e 2 e s C 600 . The 

 number of vertices is given by the relations Of, ^2r, \2r, 24r, 

 viz. 7200, 7200, 7200. 14400. By the consideration of the 

 limiting bodies (600 tO, 720 7 J 5 . 120 // for e 1 e^C m ; 600 tT, 

 1200 P 6 , 720 l\, 120 BID for e 1 e 9 C m ; 600 CO, 1200 / J 3 . 



