DERIVED FROM THE REGULAR POLYTOPES. 11 



130. Since the faces of C 24 are triangles, the coordinates of the 

 vertices of ce { C, 4 are obtained by adding the coordinates of the 

 extremities of each of the edges of C, 4 (cf. art. 117, footnote). 

 So one single symbol is found representing the vertices of ce { C, 4 . 



<*4 







2 



, 



, o 



1 24 



2 



, : 







, o 



ce^ i/,^ 



[4 ; 



, 2 : 



, 2 ; 



, o 



, Oj 9b' vertices. 



131. We obtain the coordinate-symbols of ce, 6' 24 by first 

 determining the coordinates of two adjacent vertices of an auxiliary 

 polytope ce x C' 2i obtained by adding the corresponding coordinates 

 of the vertices of the faces of C, A (cf. art. 118). 



I e 



2°. 



°24 



2 



, 2 , 



, ; 



, 



°24 



2 



, o , 



9 



, « 



^24 



2 



, o , 



: 



9 



ce, 6" 24 







, 2 ; 



2 



2 



6 24 



1 24 

 ^24 



2 

 2 







, o 



, 2 



, 



2 



, 

 , 



, Ü 



ce, C 24 



1 



; 4 



, 4 



, o 



The distance of these two vertices is found to be = 4. Hence the 

 coordinates of the vertices of ce, C , x must be multiplied by |V2 

 to obtain those of ce, C 2i . 



Two coordinate-symbols are found : 



1°. 



QÖ 



ce, 6 24 

 ce, C u 



6 , 



[3V 2 , 



2 , 

 \ 2 , 







V 2 



9 



, \ 2] . 



. 64 vertices; 



ce (ï 

 2 ^ 24 



Ce 2 24 



4 



[2V/2 , 



, 4 

 , 2V/2 , 



, 4 

 2V 2 



, 



. OJ- 

 Total . 



.32 „ ; 



. 96 vertices. 



132. In the same way we may determine the coordinates of 

 ce 3 ^24 ky introducing an auxiliary polytope whose coordinates of 

 vertices are the sums of the corresponding coordinates of the vertices 

 of each of the limiting bodies of C 2i . As the. limiting bodies are 

 octahedra, however, we may take the sums of coordinates of two 

 opposite vertices of each of them. 



