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Polytope of Type {2,24,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,3}*1152
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {2,24,3}
Number of vertices, edges, etc : 2, 96, 144, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,8,3}*384
   4-fold quotients : {2,12,3}*288
   12-fold quotients : {2,4,3}*96
   16-fold quotients : {2,6,3}*72
   24-fold quotients : {2,4,3}*48
   48-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,11)( 4,12)( 5,13)( 6,14)( 7,18)( 8,17)( 9,16)(10,15)(19,43)(20,44)
(21,45)(22,46)(23,50)(24,49)(25,48)(26,47)(27,35)(28,36)(29,37)(30,38)(31,42)
(32,41)(33,40)(34,39);;
s2 := ( 3,19)( 4,20)( 5,22)( 6,21)( 7,30)( 8,29)( 9,27)(10,28)(11,25)(12,26)
(13,24)(14,23)(15,32)(16,31)(17,33)(18,34)(37,38)(39,46)(40,45)(41,43)(42,44)
(47,48);;
s3 := ( 4, 6)( 7,16)( 8,17)( 9,18)(10,15)(12,14)(19,35)(20,38)(21,37)(22,36)
(23,48)(24,49)(25,50)(26,47)(27,43)(28,46)(29,45)(30,44)(31,42)(32,39)(33,40)
(34,41);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 3,11)( 4,12)( 5,13)( 6,14)( 7,18)( 8,17)( 9,16)(10,15)(19,43)
(20,44)(21,45)(22,46)(23,50)(24,49)(25,48)(26,47)(27,35)(28,36)(29,37)(30,38)
(31,42)(32,41)(33,40)(34,39);
s2 := Sym(50)!( 3,19)( 4,20)( 5,22)( 6,21)( 7,30)( 8,29)( 9,27)(10,28)(11,25)
(12,26)(13,24)(14,23)(15,32)(16,31)(17,33)(18,34)(37,38)(39,46)(40,45)(41,43)
(42,44)(47,48);
s3 := Sym(50)!( 4, 6)( 7,16)( 8,17)( 9,18)(10,15)(12,14)(19,35)(20,38)(21,37)
(22,36)(23,48)(24,49)(25,50)(26,47)(27,43)(28,46)(29,45)(30,44)(31,42)(32,39)
(33,40)(34,41);
poly := sub<Sym(50)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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