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Polytope of Type {57,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {57,6}*912
if this polytope has a name.
Group : SmallGroup(912,207)
Rank : 3
Schlafli Type : {57,6}
Number of vertices, edges, etc : 76, 228, 8
Order of s0s1s2 : 76
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {57,6,2} of size 1824
Vertex Figure Of :
   {2,57,6} of size 1824
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {19,2}*76
   19-fold quotients : {3,6}*48
   38-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {57,12}*1824, {114,6}*1824
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);;
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*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(76)!( 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(76)!( 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(76)!( 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);
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*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 >; 
 
References : None.
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