Polytope of Type {2,57,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,57,6}*1824
if this polytope has a name.
Group : SmallGroup(1824,1245)
Rank : 4
Schlafli Type : {2,57,6}
Number of vertices, edges, etc : 2, 76, 228, 8
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 : {2,19,2}*152
   19-fold quotients : {2,3,6}*96
   38-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7,75)( 8,77)( 9,76)(10,78)(11,71)(12,73)(13,72)(14,74)(15,67)
(16,69)(17,68)(18,70)(19,63)(20,65)(21,64)(22,66)(23,59)(24,61)(25,60)(26,62)
(27,55)(28,57)(29,56)(30,58)(31,51)(32,53)(33,52)(34,54)(35,47)(36,49)(37,48)
(38,50)(39,43)(40,45)(41,44)(42,46);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,75)(12,76)(13,78)(14,77)(15,71)(16,72)
(17,74)(18,73)(19,67)(20,68)(21,70)(22,69)(23,63)(24,64)(25,66)(26,65)(27,59)
(28,60)(29,62)(30,61)(31,55)(32,56)(33,58)(34,57)(35,51)(36,52)(37,54)(38,53)
(39,47)(40,48)(41,50)(42,49)(45,46);;
s3 := ( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)(39,42)
(43,46)(47,50)(51,54)(55,58)(59,62)(63,66)(67,70)(71,74)(75,78);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 4, 5)( 7,75)( 8,77)( 9,76)(10,78)(11,71)(12,73)(13,72)(14,74)
(15,67)(16,69)(17,68)(18,70)(19,63)(20,65)(21,64)(22,66)(23,59)(24,61)(25,60)
(26,62)(27,55)(28,57)(29,56)(30,58)(31,51)(32,53)(33,52)(34,54)(35,47)(36,49)
(37,48)(38,50)(39,43)(40,45)(41,44)(42,46);
s2 := Sym(78)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,75)(12,76)(13,78)(14,77)(15,71)
(16,72)(17,74)(18,73)(19,67)(20,68)(21,70)(22,69)(23,63)(24,64)(25,66)(26,65)
(27,59)(28,60)(29,62)(30,61)(31,55)(32,56)(33,58)(34,57)(35,51)(36,52)(37,54)
(38,53)(39,47)(40,48)(41,50)(42,49)(45,46);
s3 := Sym(78)!( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)
(39,42)(43,46)(47,50)(51,54)(55,58)(59,62)(63,66)(67,70)(71,74)(75,78);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3 >;

to this polytope