DERIVED FROM THE REGULAR POLYTOPIES. 



ce 1 I , 2 + %e , 



1 2 , I + e ', 



e 



■j 7 [2 , 3 -f 3<? , 0] : 2 12 vertices; 



ce 1 I 2 , 3 -\- e , 1 -\- e 

 I 2 , 1 -j-e , 



e x I [4 , 4 + 2e , 1 + e] : 2 24 



6-^7 2, , 3 -f e , 1 -f- e 



/ 0,2 , 1 -j- e 



e l I [2- , 5 -f e , 2 -f- 2e] : 2 24 



Total ... 60 vertices. 



120. The deduction of e 2 I from cr 2 7 and 7 is effected in the 

 same manner as that of e x I from ce x I and 7; 



«? 2 7 2 , , 3 -[- e 



I 1 + e , , 



•■> 



<? 2 7 [8 -f- e , , 5 -f- e] : 2 12 vertices 



ce 2 I 2 ,0,3 —J— f 



7 , 2 , 1 -f e 



e 2 I [2 , 2 , 4 -f- 2<?] 24 „ ; 



ce 2 I 1 4~ . e , 1 -f- e , 1 -f- e 



I 2 , 1 -j-<? , 



<? 2 7 [3 -f e , 2 -f 2e , 1 -f e] : 2. . . 24 



Total ... 60 vertices. 



121. To obtain ce { e 2 I from ce 2 I and ce 1 1 we must add to 

 the coordinates of each of the vertices of ce 2 I those of a vertex 

 of ce l obtainable from two of the three vertices of 7 from which 

 the vertex of ce 2 I can be formed. Instead of the coordinates 

 of a ce 2 7 vertex however we prefer to write separately the two 

 icosahedron-vertices from which it can be obtained by addition : 



