f) G ANALYTICAL TREATMENT OE THE POLYTOPES REGULARLY 



Case ce l eç,e. 3 e i J¥(C l6 ). Extension number 5-)-3V / 2, three net 

 symbols 



[4 + j/ 2,4 + 1/2,2 + 1/2, K2 ],(10 + 6i/2) ^ , a 2 , a s , a 4 , -Steven, 



1[d--2j/2, 3 1 , 1 ]j , S|/ 2)2a 1 + l,2fl 3 +l,2fl 8 +],2a 4 +l,la/odd, 



— J[5+ |/2,8 + K2, 1+1/2, 1+1/21)' v ~ K ; *~ 3 ~ 3T ^ 4T 'i 



l --2l/2, 3 1,1 J) / 5 I 3 ^ 2 ) 2ûh + 1, 2a» +1, 2« 3 + 1, 2a. + 1, i«; even, 



£[5+ 1/2, 3 + 1/2, 1 + 1/2, l + i/2J v ~ y J in ^ 3 ~ 3T iT ^ 



which are to be reduced to the new origins, to be formed according 

 to the indications of the preceding example. Here the polytope of 

 edge import is lacking. In the case of the body gap we mention 

 only the first net symbol and the lower part of the third, which 

 lead to the desired result. 

 Body gap prism. We find 



[4 + 1/2,4 + 1/2, 2 + 1/2, 1/2 ], (5 + 31/2) 2^ — £, 2« 3 — |, 2a s — \, 2« 4 — \ , Sa-, even, 



l 



J[5 — j/2, 3 + 1/2, 1 + 1/2, l+j/2], (5 + 3|/2)2a 1 + i,20 8 + 4,2« s + i,2« 4 + *, ^a» even, 



l 



giving by means of the substitutions a i = 0, (i = 1, 2, 3,4), the 

 prism P tTi the two bases of which are 



Q 



( 



3 — 1/2 3 — 1/2 —1 — 1/2 —5—1/2 



2~ ~1T ~~2~~ ~ 2~ 



3 + 1^2 3-1-1/2 — l-f-i/2 — 5 + J/2 



> 



2 2 7 2 



Face gap prismotope. Here we have 



2 



> 



[4+ |/2,4 + ^/2,2 + l/2, 1/2 ], (5 + 3j/2) 2a x — |,2«g — f, 2a 8 — f,2« 4 ,2"^ even, 



l 



1 [5 _|_ y 2, 3 + j/2^ 1 + 1/2,' 1 + 1/2] ' ^ ~*~ 8 ^ 2) 2rtl ^~ *• 2 ^ ^"~ *' 2% ^~ *' 2 ^+ X ' f ^ ° dd ' 

 l r k _j_ «: 



I |5_i_2jX2 3 "i) 4 



| ,5 _| ^1 3 + j/2,' 1 + 1/2.' 1 + 1/2] ' (5 + 3K2 ^ 2fl * + h 2a * + *' 2 ^ 3 + *' 2a 4+ lj f tt < even ' 



giving by means of the suitable substitutions easily found 

 (f — V2, f — V2, — A_v/2) [V2] 



(f+\Z2, f + V/2 



v 3 



(f + V/2, Ï + V2 



( 2l 2 



v a > ~r 



— 4 + V/2)— 1/2 



— | )_2\/2 



— -f + N/2) V/2 



— 4 ) 2V2 



which can be telescoped into 



