Polytope of Type {2,68,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,68,6}*1632b
if this polytope has a name.
Group : SmallGroup(1632,1195)
Rank : 4
Schlafli Type : {2,68,6}
Number of vertices, edges, etc : 2, 68, 204, 6
Order of s₀s₁s₂s₃ : 102
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) :
   17-fold quotients : {2,4,6}*96b
   34-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)( 7,69)( 8,70)( 9,67)(10,68)(11,65)(12,66)(13,63)(14,64)
(15,61)(16,62)(17,59)(18,60)(19,57)(20,58)(21,55)(22,56)(23,53)(24,54)(25,51)
(26,52)(27,49)(28,50)(29,47)(30,48)(31,45)(32,46)(33,43)(34,44)(35,41)(36,42)
(37,39)(38,40);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,67)(12,69)(13,68)(14,70)(15,63)(16,65)
(17,64)(18,66)(19,59)(20,61)(21,60)(22,62)(23,55)(24,57)(25,56)(26,58)(27,51)
(28,53)(29,52)(30,54)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)(38,46)
(40,41);;
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);;
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*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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