Polytope of Type {2,69,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,69,4}*1104
if this polytope has a name.
Group : SmallGroup(1104,162)
Rank : 4
Schlafli Type : {2,69,4}
Number of vertices, edges, etc : 2, 69, 138, 4
Order of s₀s₁s₂s₃ : 138
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) :
   23-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7,91)( 8,93)( 9,92)(10,94)(11,87)(12,89)(13,88)(14,90)(15,83)
(16,85)(17,84)(18,86)(19,79)(20,81)(21,80)(22,82)(23,75)(24,77)(25,76)(26,78)
(27,71)(28,73)(29,72)(30,74)(31,67)(32,69)(33,68)(34,70)(35,63)(36,65)(37,64)
(38,66)(39,59)(40,61)(41,60)(42,62)(43,55)(44,57)(45,56)(46,58)(47,51)(48,53)
(49,52)(50,54);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,91)(12,92)(13,94)(14,93)(15,87)(16,88)
(17,90)(18,89)(19,83)(20,84)(21,86)(22,85)(23,79)(24,80)(25,82)(26,81)(27,75)
(28,76)(29,78)(30,77)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)(38,69)
(39,63)(40,64)(41,66)(42,65)(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)(49,58)
(50,57)(53,54);;
s3 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)
(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)
(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81)(83,86)(84,85)(87,90)
(88,89)(91,94)(92,93);;
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, s3*s2*s1*s3*s2*s3*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*s1*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*s1*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*s1*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*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(94)!(1,2);
s1 := Sym(94)!( 4, 5)( 7,91)( 8,93)( 9,92)(10,94)(11,87)(12,89)(13,88)(14,90)
(15,83)(16,85)(17,84)(18,86)(19,79)(20,81)(21,80)(22,82)(23,75)(24,77)(25,76)
(26,78)(27,71)(28,73)(29,72)(30,74)(31,67)(32,69)(33,68)(34,70)(35,63)(36,65)
(37,64)(38,66)(39,59)(40,61)(41,60)(42,62)(43,55)(44,57)(45,56)(46,58)(47,51)
(48,53)(49,52)(50,54);
s2 := Sym(94)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,91)(12,92)(13,94)(14,93)(15,87)
(16,88)(17,90)(18,89)(19,83)(20,84)(21,86)(22,85)(23,79)(24,80)(25,82)(26,81)
(27,75)(28,76)(29,78)(30,77)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)
(38,69)(39,63)(40,64)(41,66)(42,65)(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)
(49,58)(50,57)(53,54);
s3 := Sym(94)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)
(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)
(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81)(83,86)(84,85)
(87,90)(88,89)(91,94)(92,93);
poly := sub<Sym(94)|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, 
s3*s2*s1*s3*s2*s3*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*s1*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*s1*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*s1*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*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope