Polytope of Type {57,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {57,6,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1245)
Rank : 4
Schlafli Type : {57,6,2}
Number of vertices, edges, etc : 76, 228, 8, 2
Order of s₀s₁s₂s₃ : 76
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) :
   12-fold quotients : {19,2,2}*152
   19-fold quotients : {3,6,2}*96
   38-fold quotients : {3,3,2}*48
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)( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32)(33,36)(37,40)
(41,44)(45,48)(49,52)(53,56)(57,60)(61,64)(65,68)(69,72)(73,76);;
s3 := (77,78);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(78)!( 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(78)!( 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(78)!( 1, 4)( 5, 8)( 9,12)(13,16)(17,20)(21,24)(25,28)(29,32)(33,36)
(37,40)(41,44)(45,48)(49,52)(53,56)(57,60)(61,64)(65,68)(69,72)(73,76);
s3 := Sym(78)!(77,78);
poly := sub<Sym(78)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2 >;

to this polytope