Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,69,4}

Atlas Canonical Name {2,69,4}*1104

Overview

Group
SmallGroup(1104,162)
Rank
4
Schläfli Type
{2,69,4}
Vertices, edges, …
2, 69, 138, 4
Order of s0s1s2s3
138
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

23-fold

Covers minimal covers in bold

None in this atlas.

Representations

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 >;