82 ANALYTICAL TREATMENT OF THE POLYTOPES REGULARLY 



as the number of vertices is 2 5 . 6! divided by 2 2 , i.e. 5760, 

 we set in toto 



7.5760 



•> 



i.e. 20160(0!, 



~ 



^ =57r)0A) l ^ i0 = 14400 A) 6 ^ = 5760^ „ 25920(/)„ 



!™ = 5 1 5760 =2400 6 1 5760 = 576 

 10 12 6 



^==3840^,^ = 14400, 



4 5760 



= 960^(9 „ 14880(/) 3 , 



24 



2.5760 Q cr^ 5760 io 9 ^ 



— —-=192^^3^(5),-— -—=192^ <? 2 <S(o), 

 00 oU 



^=4S0,, o ,^240, CO) 



^ = 640(3 ; 3), 2 ^ = 640(3 ; 6), 

 2.5760 



= l20ce ± e 2 C ±fi . „ 3656(/) 4> 



96 



5760 qo 5760 



-yg^^ 32^,^ #(6),-^- = 160 (#, ; tf 7 ), 



2.5760 „_ 5760 



ce i p 2 We 4 8 

 = 32e 1 <? 2 * 4 fl(fl) ,, 296(/) 5 . 



192 # ^ï^We' 480 



2.5760 



360 

 So the result is, in accordance with the law of Euler, 



(5760, 20160, 25920, 14880, 3656, 296). 



The results obtained in this way are tabulated in Tables VIII and IX. 



Table VIII, concerned with the hnpd. in S s , #4, $ 5 , has been 

 divided vertically into six main parts, giving respectively the ex- 

 pansion symbol, the symbol of coordinates, the symbol of charac- 

 teristic numbers, the faces, the limiting polyhedra, the limiting 

 polytopes. The part of the faces is split up into three columns 

 successively related to triangular, square, hexagonal faces; likewise 

 that of the limiting bodies is split up into seven columns corres- 

 ponding to the seven possibilities 1\ 0, P s , tT, CO, i J 6 , tO. Of the 

 two numbers given in any case the first always indicates the total 



