LIST OF POLYTOPES DEDUCED FROM MEASURE POLYTOPE AND CROSS POLYTOPE. 



>i = 3 



Table IV. 



C 



e, C= tC 



e, G=BGO 



e, e 2 C == ^CO 



ce, C = CO 



ce 2 C = O 



ce 4 e, C = I O 



ce 2 O 



ce, e, O 



e 2 O 



e, e 2 O 



,ce, O 



O 



e, O 



[111] 

 [ l'l'l ] 

 [ 1' 1 1 ] 



[ 2' ri ] 



[110] V/2 

 [100] V/2 



[210] V'2 



( 8 d 12, 6,) 



(24, 36, 14 2 ) 



(24, 48 2 26 3 ) 



(48, 72 3 2G 3 ) 



(12, 24, 14.,) 



( 6, 12, 8,) 



(24, 30., 14,) 



1 



12 



Pi 



Vk 





P-i 

 Pe 



1 



2, 1 



3, 1 

 1 



2, 1 



3, 1 



;/ = 4 





G 



?i 



Cs 



e. 



Cs 



e-i 



c s 



e, e. 



C* 



e, e 3 



Cs 



e, e 3 



Cs 



e, e 2 e 3 



Cs 



ce, 



Cs 



ce. 



Cs 



c<? 3 



Cs 



ce, e. 



Cs 



CC', e 3 



Cs 



ce 2 e, 



Cs 



ce, e 2 e 3 



Cs 



ce 3 6, 6 



cc, c 3 C, 



ce, e 3 C, 6 



c 3 C i6 



ce. e, e 3 C, 6 



e-i e 3 C K 



ei e 3 C m 



e, e, e 3 C, 6 



c e 2 C, 



C,,, = cc, C, 6 



C|6 



ce, c 2 C, 6 



e 2 C 1G 



«i '"in 



e, e, C, 6 



[1111] 

 [l'l'l'l] 

 [l'l'l 1] 

 [l'lll] 

 [ 2'2'1'1 ] 

 [2'1'1'1] 

 [2'1'1 1] 

 [3'2'1'1] 

 [1110] V'2 

 [1100] V2 

 [1000] V'2 

 [2210] V/2 

 [2 110] V/2 

 [2100] V/2 

 [3210] V 2 



( 16, 



32, 



24, 



80 



( 64, 



128, 



88. 2 



24g) 



( 96, 



2SS 2 



248 4 



56 3 ) 



( 64, 



192, 



20 8 3 



80 t ) 



(192, 



384,, 



248,, 



56 3 ) 



(192, 



480 3 



36 8 5 



80 4 ) 



(192, 



4 80 3 



368 6 



800 



(384, 



768 t 



464 6 



800 



( 32, 



96, 



88 2 



24 2 ) 



( 24, 



96, 



96, 



240 



( 8, 



24, 



32, 



160 



( 96, 



1Q2 2 



120 3 



24 2 ) 



( 90, 



288 2 



240 4 



480 



( 48, 



120 2 



90, 



24,) 



(192, 



384 3 



240, 



48 3 ) 



24 



32 



16 



te 











T 



RCO 



— 



P a 



O 



c 



1\ 



P 3 



T 



tco 



— 



Pz 



tT 



te 



Pb 



p. 



CO 



RCO 



A 



p e 



tT 



tco 



Pb 



p* 



10 



CO 



— • 



— 



T 







— 



— 



O 



T 

 tT 



to 











co 



A 



— 



CO 







— 



— 



tT 



to ' 



P* 



— 



to 



1 



2, 1 



3, 2, 1 



3, 1 



4, 2, 1 

 5,3, 1 

 6, 3, 1 

 1 



2, 1 



3, 2, 1 



3, 1 



4, 2, 1 



5, 3, 1 



6, 3, 1 



1 



3, 1 

 2,1 

 1 

 3, 1 





e,,. 



e, 



C\n 



e 2 



t-h> 



H 



Cii) 



c h 



^10 



e t e 2 



t-io 



e, e 3 



L-10 



C\ e 4 



^10 



e 2 e 3 



C10 



e 2 e 4 



C ln 



03*4 



Co 



e, e 2 c 3 



C\o 



e, e 2 e 4 



C10 



e, e 3 e 4 



Cjo 



e 1 e 3 e 4 



Cio 



ci c, e 3 e 4 



^10 



cc, 



'10 



ce 2 



Cio 



ce 3 



C,o 



cc,, 



f '10 



ce, e. 



C10 



ce, c 3 



L'10 



ce, e 4 



C,o 



ce 2 e 3 



C10 



ce 2 c\ 



Cio 



ce 3 e 4 



Co 



cc, c 2 e 3 



C,0 



cc, e 2 e 4 



Cjo 



ce, e 3 e 4 



C10 



ce, e 3 e 4 



C,o 



ce, e, e 3 e„ 



Cio 





?e 4 



c 3i 



«?s 



c 4 



c f2 



ce 2 



e 4 



'32 



ce, 



<?4 



c f 





e 4 



C 3 i 



ce, e 3 



e 4 



c f 



ce, e 3 



e 4 



'32 



<?3 



c 4 



c, 2 



ce, e 2 



«4 



c 32 



e. 2 



c 4 



c tó 



«1 



Ci 



c 32 



e, e, e 3 



e 4 



^32 



e 2 e 3 



e 4 



Q« 



Ci e.. 



c 4 



c 32 



e, e. 



e 4 



C30 



e, e 2 e 3 



d. 



c 32 





;e 3 



C 3 2 



( 



;e a 



c 31 





?e, 



c 3i 

 c 32 



ce. 



<? 3 



<',: 



ce, 



c 3 



C 3 2 





e 3 



^32 



ce, 



e 2 



n 



°32 





e 2 



C32 





<?i 



c 3i 



ce, e 2 



e 3 



c 32 



e. 



e 3 



c» 



e. 



e 3 



c 32 



«i 



e 2 



c- r 



e, e. 



e 3 



^32 



11111] 

 l'l'l'l' 1] 

 l'l'l'l 1] 

 l'l'l 1 1 ] 



l'l 1 1 1 ] 



2'2'2'1' 1] 



a's'i'i'i] 



2'1' l'l'l] 

 2' 2' l'l l] 

 2' l'l'l 1] 

 2' 1' 1 1 1] 

 3' 3' 2' l'l] 

 3' 2' 2' l'l] 

 3' 2' l'l'l] 

 3' 2' l'l 1] 

 4' 3' 2' l'l] 

 11110] V/2 

 11100] V/2 

 11000] V2 

 10000] V/2 

 222 iO] V/2 

 22110] V/2 

 21110] V/2 

 22100] V/2 

 21100] V/2 

 21000] V/2 

 33210] V 2 

 322 1 0] \ 2 

 32110] V/2 

 32100] V/2 

 43210] V 2 















10 



40 



8 







80 



"J-'l 



80, 



SO, 



40, 



10,) 



1 



c 8 



— 







— 



100, 



400, 



400, 



200, 



42,) 



3 



1 u 



e, G 8 



— 







— 



320, 



1280 2 



1520 4 



6S0„ 



122 3 ) 



3 

 . 1 



e, C 8 



■ — 







■ Pr 



320, 



1440 2 



2160 4 



1240 6 



2020 



3 



1 ï) 



e 3 C's 



— 



(4 



3) 



Po 



160, 



640 2 



1040 3 



800 4 



242,) 



3 

 1 



Cs 



^ J c 



(4 



3) 



Pt 



640, 



1600 3 



1520 4 



080 4 



1220 



3 

 ïïï 



e, e 2 C 8 



— 







Pt 



900, 



3360 3 



3760,; 



15G0 7 



2020 



3 

 1 



c, e 3 C's 



— 



(8 



3) 



Po 



640, 



2240 3 



2960.5 



1600 7 



242,) 



3 



1 



e, C 8 



Pu, 



(8 



3) 



Pt 



900, 



2880 3 



2960 6 



1240 6 



2020 



3 

 1 ü 



e, e 3 C's 



— 



(4 



3) 



Pr, 



900, 



3840 3 



4720, 



2080 g 



242,) 



3 

 1 



C-2 C 3 



p 



1 nco 



(4 



3) 



p 



r CO 



(340, 



2240 



28S0 S 



1520, 



2420 



3. 

 1 



e a Cs 



Pc 



(4 



6) 



Pr 



1920, 



4S00 4 



4240 7 



1500, 



2020 



3 

 1 



e, e, e 3 C 8 



— 



(S 



3) 



Pr 



1920, 



5700,, 



6000 8 



2400 8 



242 5 ) 



3 

 1 ü 



e, e 2 C 8 



p 



-L (CO 



(8 



3) 



Pco 



1920, 



5760 4 



5760 8 



2160 9 



242,) 



3 



e, e, C e 



Pw 



(8 



6) 



P,r 



1920, 



5760 4 



5920 8 



2320 9 



242,) 



3 

 1 ü 



e, e 3 C 8 



p 



r nco 



(4 



6) 



P,o 



3840, 



90 00, 



8160,, 



2640,, 



242,) 



3 

 1 U 



e, e, e 3 C 8 



p 



1 tco 



(8 



6) 



P,o 



80, 



320, 



400. 2 



200 2 



42,) 



2 

 5 



ce, C s 



— 







— 



80, 



480, 



640, 



280 3 



42 2 ) 



1 

 2 



ee 2 C 8 



— 







— 



40, 



240, 



400, 



240, 



42,) 



1 



ce 3 C 8 



— 







— 



10, 



40, 



80, 



80, 



32;) 



ï 



— 



— 







— 



320, 



800 2 



720 3 



280 3 



42 2 ) 



3 



1 ü 



ce, e, C's 



— 







— 



480, 



1920, 



2160., 



840, 



1 22 3 ) 



3 

 1 Ü 



ce, e 3 C 8 



— 



(4 



3) 



— 



320, 



1440, 



2160,, 



1200 6 



162 4 ) 



3 

 1 



ce x C's 



Pco 



(4 



3) 



— 



160, 



480 2 



560., 



280 3 



42 2 ) 



3 



1 (I 



ce 2 e 3 C's 



— 







— 



240, 



1200 2 



1520 4 



640,, 



82 3 ) 



3 



1 



ce 2 C 8 



Po 







— 



80, 



2 SO, 



400, 



240, 



42 2 ) 



3 

 1 ü 



ce 3 C 8 



— 







— 



960, 



2400a 



2100, 



840 6 



122,) 



3 

 1 



ce, e 2 e 3 C ( 



— 



(4 



3) 



— 



960, 



2sMi ; , 



2900,; 



1200 6 



162,,) 



3 

 1 ü 



ce, e 2 C 8 



P,o 



(4 



3) 



— 



960, 



3360 3 



3680,; 



1440, 



162„) 



3 



1 ü 



ce, e 3 Cg 



p 



r co 



(4 



6) 



— 



480, 



1440., 



1520, 



640 4 



82 3 ) 



3 

 1 



ce 2 c 3 C 8 



Po 







— 



1920, 



4800„ 



4160, 



1440, 



1620 



3 

 .1 



ce e, e 3 ( 8 



l\„ 



(4 



6) 



— 



32 



1 



S{ö) 



r 



ce, S (5) 



1' 



ce, S (5) 



1' 



S '(5) 



1' 



e, S{5) 



2' 



e, -S (5) 



2' 



e 3 £(5) 



2' 



ce, e, S (5) 



2' 



e.,S(b) 



2' 



e, tf(5) 



2' 



e, e, S(o) 



3' 



e, e 3 S(b) 



3' 



e,e 3 ,V(5) 



3' 



e, e, <y(5) 



3' 



e, e, e : , /S' (5) 



4' 



5(5) 



1" 



ce, /S* (5) 



1" 



ce, 5(5) 



1" 



5(5) 



1" 



e,5(5) 



2" 



e, 5(5) 



2" 



e 3 5(5) 



2" 



ce, e, 5(5) 



2" 



e, 5(5) 



2" 



e, 5(5) 



2" 



e, e 2 5(5) 



3" 



e,e 3 5(5) 



3" 



e, e 3 5(5) 



3" 



e, e, 5(5) 



3" 



e, e, e 3 5(5) 



1" 



, 1 





, 2, 1 





, 3, 2, l 





, 1 





,2,1 





, 3, 2, 1 





,3, 1 





, 4, 2. 1 





, 5, 3, 1 





,3, 1 





, 4, 2, 1 





, 5, 3, 1 





, 6, 3, 1 





,6,3,1 







4 



, 1 



3 



, 2, 1 



2 



, 3, 2, 1 



1 



, 1 



7 



, 2, 1 







, 3, 2, 1 



5 



,3, 1 



5 



, 4, 2, 1 



4 



, 5, 3, 1 



3 



.3, 1 



9 



, 4, 2, 1 



8 



, 5, 3, 1 



7 



,6,3, 1 







, 6, 3, 1 



10 



3, 2, 1 



2, 1 

 1 



5, 3, 1 



4, 2, 1 



3, 2, 1 



3, 1 



2, 1 

 1 

 6,3, 1 



5, 3, 1 



4, 2, 1 



3, 1 



6, 3, 1 



