Polytope of Type {6,57,2}

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

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

Permutation Representation (Magma) :

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

to this polytope