DERIVED FROM THE REGULAR POLTTOJfES. 19 



720 7%, 120 tD for e 2 a^C (m ; 600 tO, 1200 1\. , 720 P 10 , 

 120 f ID for ^^2^3 C 600 ) we obtain consecutively for tlie limiting 

 bodies 1440, 2640, 2640, 2640 and for the faces 8640, 13440, 

 13440, 17040. This gives 



e x e 2 C im ( 7200 , 14400 , 8640 , 1440) 



*1 «8^600 ( 720ü ' 180()0 ' 13440 ' 264 °) 



Hh C &W ( 7200 > I 8000 ' 13440 ' 2G4 °) 



*i «2*3^600 (14400 , 28800 , 17040 , 2640). 



147. Forms ce x 6g 0() , ce 2 C 600 , cc à C G0Q . The numbers of vertices 

 are 1 1440, I. 3600, 1 2400, 'viz. 720, 1200, 600. By the 

 consideration of the limiting bodies (600 O, 120 I for ce l C 600 ; 

 600 T, 120 ID for ce 2 C 600 ; 120. D for c<? 3 £ 6Ö0 ) we obtain for 

 the limiting bodies 720, 720, 120 and for the limiting faces 

 3600, 3120, 720. This gives 



Ce i ^600 



( 720 , 



3600 , 



3600 , 



720) ; 



op C 



te 2 ' 600 



(1200 , 



3600 , 



3120 , 



720) ; 



ce a 



( 600 , 



1200 , 



720 , 



120) . 



148. forms ce { e t C GUI1 , ce 1 e 3 ' (;(ll , , cr 2 c s ^500 > c ^i e 2 e 3 ^600 • 

 B\ the c-operation the bodies of body-import 10', tl\ CO, tO, 

 arc transformed into tl\ O, T, IT, and accordingly (>/', 12/-, 

 12 r, 21 y become 3/, 6/-, 4r, 12 r leading to 3600, 3600, 

 2400, 7200 vertices. By the consideration óf the limiting bodies 

 (600 IT, 120 tl for ce l e 2 C m) ; 600 O, 1200 P 3 , 120 7.7/; 

 for ce l g s C m ; 600 7', 120 W for cé? 2 <? 3 (7 600 ; 600 />. 1200 /'.. . 

 120 ///J for ce l e 2 e s Q 00 ) we obtain for the limiting bodies 720, 

 1920. 720. 19.20 and for the limiting faces 4320. 9120. 3120, 

 9120. This gives 



ce x e 2 6 600 



(3000 , 



7200 , 



4320 , 



720) 



ce \ e S 600 



(3600 , 



10800 , 



91.20 , 



1920) 



ce 2 '':! 600 



(2400 , 



L800 , 



3120 , 



720) 



Ce ] r -l r -A ' CI 1(1 



(7200 . 



14100 . 



9120 , 



1920) 



V. 'I he coordinates of the C^-family. 



I 19. To deduce the coordinate-symbols of the polytopes.of the 

 (7 600 -family we may choose as the „patriarch" (art. 48) of the 



