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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}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97552)
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}*128a
   18-fold quotients : {2,4,4}*64, {2,8,2}*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 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)
(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)(23,67)
(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)(34,65)
(35,64)(36,60)(37,62)(38,61);;
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)(39,61)(40,58)(41,64)(42,60)(43,57)(44,63)
(45,62)(46,59)(47,65)(48,70)(49,67)(50,73)(51,69)(52,66)(53,72)(54,71)(55,68)
(56,74);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(60,63)(61,64)(62,65)
(69,72)(70,73)(71,74);;
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, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)
(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,66)(22,68)
(23,67)(24,72)(25,74)(26,73)(27,69)(28,71)(29,70)(30,57)(31,59)(32,58)(33,63)
(34,65)(35,64)(36,60)(37,62)(38,61);
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)(39,61)(40,58)(41,64)(42,60)(43,57)
(44,63)(45,62)(46,59)(47,65)(48,70)(49,67)(50,73)(51,69)(52,66)(53,72)(54,71)
(55,68)(56,74);
s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)(60,63)(61,64)
(62,65)(69,72)(70,73)(71,74);
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, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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