20 ANALYTICAL TREATMENT OF THE POLYTOPES REGULARLY 



family either the C 600 or the C l20 , neither of which however can 

 be represented by a single coordinate-symbol. We choose the 6' 600 , 

 as it seems to be the simplest one. 



When the length of the edge is assumed to be = 4 , the C m) 

 can be represented by three coordinate-symbols *) 



[2 i + 2e , , , ] 8 



[3 -f e ' , 1 4- e , 2 , ] : 2 96 



[1 + e , 1 + e , 1 -J- e , 1 -f e] J6_ 



120 



where e == V 5 and : 2 denotes pentagonal hemiedry (cf. art. 116). 

 The numbers on the right side are the numbers of vertices repre- 

 sented by each of the symbols. 



150. From C 60l) we first deduce the other primitive forms of 

 the family ee l <7 600 , ce 2 Q 00 and ce ;i C m = C\ 20 . 



Since the faces of C' 600 are triangles, the coordinates of the 

 vertices of ce^ (' m) are obtained by adding those of two adjacent 

 vertices of (7 600 (see art. 117, foot-note). 



Six coordinate symbols are obtained. 2 ) 



^600 

 ^600 



.2 -f 2e 

 3 + * 



o 



1 -\-e 



, o , 



2 , 













Ce l ^600 



^600 

 °600 



[5 + 3e 



3 -\-è 



3 + <> 



1 -j-e 



i 4-* 



2 , 



, 2 , 

 . —2 , 









 



] 



^600 

 "600 



[6 + 2 e 



3 -\-e 

 S-{~e 



2 4- 2e 



l.+ e 

 



, o , 



, 2 , 



. 1 +e . 











2 



] 



ce \ ^600 



[6 + 2e 



i 4-e 



. 3 4-* , 



2 



] 



96 



48 



192 



') P. H. Schoute. Mehrdimensionale Geometrie II, § 7, art. 69, p. 209. 



P. H. Schoute. Regelmiissige Sohnitte und Projectionen des Hundertzwanzigzelles 

 und Seehshundertzelles im vicrdimensionalen Raume. Verb., der Kon. Akad. v. W. te 

 Amsterdam. Eerste sectie. Deel II, n c . 7. Tabelle I A. 



E. L. Elte. The semiregular Polytopes of the hyperspaces (Dissertation, Groningen 

 L912) § 15, p. 23; Table E, p. 28 (multiplied by £ (5 + e)). 



*) Elth. Diss. § 15, p. 24, Table A; § 16, p. 31 Table H, the last six symbols 

 (multiplied by 5 -f- e). 



