Polytope of Type {2,76,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,76,6}*1824b
if this polytope has a name.
Group : SmallGroup(1824,1245)
Rank : 4
Schlafli Type : {2,76,6}
Number of vertices, edges, etc : 2, 76, 228, 6
Order of s₀s₁s₂s₃ : 114
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,4,6}*96b
   38-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope