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Polytope of Type {2,24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98807)
Rank : 4
Schlafli Type : {2,24,4}
Number of vertices, edges, etc : 2, 72, 144, 12
Order of s0s1s2s3 : 8
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) :
   2-fold quotients : {2,12,4}*576
   4-fold quotients : {2,6,4}*288
   8-fold quotients : {2,6,4}*144
   9-fold quotients : {2,8,4}*128b
   18-fold quotients : {2,4,4}*64
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,48)( 4,50)( 5,49)( 6,54)( 7,56)( 8,55)( 9,51)(10,53)(11,52)(12,39)
(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,57)(22,59)(23,58)
(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)
(35,73)(36,69)(37,71)(38,70);;
s2 := ( 3, 7)( 5,10)( 8, 9)(12,16)(14,19)(17,18)(21,34)(22,31)(23,37)(24,33)
(25,30)(26,36)(27,35)(28,32)(29,38)(39,70)(40,67)(41,73)(42,69)(43,66)(44,72)
(45,71)(46,68)(47,74)(48,61)(49,58)(50,64)(51,60)(52,57)(53,63)(54,62)(55,59)
(56,65);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)
(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);;
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*s2*s3, s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2, 
s3*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 3,48)( 4,50)( 5,49)( 6,54)( 7,56)( 8,55)( 9,51)(10,53)(11,52)
(12,39)(13,41)(14,40)(15,45)(16,47)(17,46)(18,42)(19,44)(20,43)(21,57)(22,59)
(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)
(34,74)(35,73)(36,69)(37,71)(38,70);
s2 := Sym(74)!( 3, 7)( 5,10)( 8, 9)(12,16)(14,19)(17,18)(21,34)(22,31)(23,37)
(24,33)(25,30)(26,36)(27,35)(28,32)(29,38)(39,70)(40,67)(41,73)(42,69)(43,66)
(44,72)(45,71)(46,68)(47,74)(48,61)(49,58)(50,64)(51,60)(52,57)(53,63)(54,62)
(55,59)(56,65);
s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)
(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);
poly := sub<Sym(74)|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*s2*s3, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2, 
s3*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 >; 
 

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