Polytope of Type {2,51,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,51,6}*1632
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 4
Schlafli Type : {2,51,6}
Number of vertices, edges, etc : 2, 68, 204, 8
Order of s₀s₁s₂s₃ : 68
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 : {2,17,2}*136
   17-fold quotients : {2,3,6}*96
   34-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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