Polytope of Type {2,6,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,51}*1632
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 4
Schlafli Type : {2,6,51}
Number of vertices, edges, etc : 2, 8, 204, 68
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 : {2,2,17}*136
   17-fold quotients : {2,6,3}*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)( 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);;
s2 := ( 5, 6)( 7,67)( 8,68)( 9,70)(10,69)(11,63)(12,64)(13,66)(14,65)(15,59)
(16,60)(17,62)(18,61)(19,55)(20,56)(21,58)(22,57)(23,51)(24,52)(25,54)(26,53)
(27,47)(28,48)(29,50)(30,49)(31,43)(32,44)(33,46)(34,45)(35,39)(36,40)(37,42)
(38,41);;
s3 := ( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,70)(12,68)(13,69)(14,67)(15,66)(16,64)
(17,65)(18,63)(19,62)(20,60)(21,61)(22,59)(23,58)(24,56)(25,57)(26,55)(27,54)
(28,52)(29,53)(30,51)(31,50)(32,48)(33,49)(34,47)(35,46)(36,44)(37,45)(38,43)
(39,42);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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