( 694 ) 



1 (2) 



10 



— Mb = 

 10 



O , 



//■^ 



.(O 



3 ' 



10 V 8 8 ; 5 ' 



1 f2) 



5 



2 f2) 



-Mr/ 



1 \ f2; (2) 



f2) 1 f4) 



4 ' 4 y 2 ' 



7 f2) 9 (2) 



whilst the forms appearing past tiie middle yrMr, ,—^M-, and 



3 ,,-(2) 4 (2) • r . 1 1 /''^ r^''^ 



— 7)75 , — Mb of opposite orientation arc indicated by /_2, /_! 

 5 5 



(2) ^ (2) 



and 7'_2 , 7'_i . 



By considering the trnncated fivecells qS(jj) we tind immeditately : 



(1) 



.w 



Of tiiese relations e. g. the last one is deduced in the following 



{k) 3 (hk) 

 way : The form I^ == — S appears by trnncating the fivecell 



5 



S ^= 1 \ to ^ of the edges. As each two of the five poly topes 

 5 



J^^) (3^0 , . , 



,S ^= J \ , which are taken off bj the truncation, have an 



>S = /i m common, we subtract when diminishing li by 



5 Yi {qw times /i too much. 



Together the equations (1) lead to the relations of volume: 



,(2A) 



7 I J 1 



1 



16 



(k) 

 76 



(2/0 

 T2 



176 



Ale) 

 7 3 



i2 



230 384 



where 7^('^^) is the rhombotope formed by the required stretching of 



(2/;) 



an M4 in the direction of a diagonal. If the number 384 is 



^pk) 1 (2/1-) 



deduced from the remark that 7\ = — R , then the two relations 



4! 



2(16 + 176) = 384 , 2 (1 + 76) -f 230 = 384, 



