Polytope of Type {57,4,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {57,4,2,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1247)
Rank : 5
Schlafli Type : {57,4,2,2}
Number of vertices, edges, etc : 57, 114, 4, 2, 2
Order of s0s1s2s3s4 : 114
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   19-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5,73)( 6,75)( 7,74)( 8,76)( 9,69)(10,71)(11,70)(12,72)(13,65)
(14,67)(15,66)(16,68)(17,61)(18,63)(19,62)(20,64)(21,57)(22,59)(23,58)(24,60)
(25,53)(26,55)(27,54)(28,56)(29,49)(30,51)(31,50)(32,52)(33,45)(34,47)(35,46)
(36,48)(37,41)(38,43)(39,42)(40,44);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,73)(10,74)(11,76)(12,75)(13,69)(14,70)
(15,72)(16,71)(17,65)(18,66)(19,68)(20,67)(21,61)(22,62)(23,64)(24,63)(25,57)
(26,58)(27,60)(28,59)(29,53)(30,54)(31,56)(32,55)(33,49)(34,50)(35,52)(36,51)
(37,45)(38,46)(39,48)(40,47)(43,44);;
s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)
(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)
(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)
(65,68)(66,67)(69,72)(70,71)(73,76)(74,75);;
s3 := (77,78);;
s4 := (79,80);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(80)!( 2, 3)( 5,73)( 6,75)( 7,74)( 8,76)( 9,69)(10,71)(11,70)(12,72)
(13,65)(14,67)(15,66)(16,68)(17,61)(18,63)(19,62)(20,64)(21,57)(22,59)(23,58)
(24,60)(25,53)(26,55)(27,54)(28,56)(29,49)(30,51)(31,50)(32,52)(33,45)(34,47)
(35,46)(36,48)(37,41)(38,43)(39,42)(40,44);
s1 := Sym(80)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,73)(10,74)(11,76)(12,75)(13,69)
(14,70)(15,72)(16,71)(17,65)(18,66)(19,68)(20,67)(21,61)(22,62)(23,64)(24,63)
(25,57)(26,58)(27,60)(28,59)(29,53)(30,54)(31,56)(32,55)(33,49)(34,50)(35,52)
(36,51)(37,45)(38,46)(39,48)(40,47)(43,44);
s2 := Sym(80)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)
(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)
(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)
(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75);
s3 := Sym(80)!(77,78);
s4 := Sym(80)!(79,80);
poly := sub<Sym(80)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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