Polytope of Type {6,76}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,76}*912b
if this polytope has a name.
Group : SmallGroup(912,207)
Rank : 3
Schlafli Type : {6,76}
Number of vertices, edges, etc : 6, 228, 76
Order of s₀s₁s₂ : 57
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,76,2} of size 1824
Vertex Figure Of :
   {2,6,76} of size 1824
Quotients (Maximal Quotients in Boldface) :
   19-fold quotients : {6,4}*48b
   38-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,76}*1824
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, 7)( 3, 6)( 4, 5)( 9,76)(10,75)(11,74)(12,73)(13,72)(14,71)
(15,70)(16,69)(17,68)(18,67)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)(25,60)
(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)(33,52)(34,51)(35,50)(36,49)
(37,48)(38,47)(39,46)(40,45)(41,44)(42,43);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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 >;

References : None.
to this polytope