Part of the Atlas of Small Regular Polytopes

Polytope of Type {69,4,2}

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

Overview

Group
SmallGroup(1104,162)
Rank
4
Schläfli Type
{69,4,2}
Vertices, edges, …
69, 138, 4, 2
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 := ( 2, 3)( 5,89)( 6,91)( 7,90)( 8,92)( 9,85)(10,87)(11,86)(12,88)(13,81)(14,83)(15,82)(16,84)(17,77)(18,79)(19,78)(20,80)(21,73)(22,75)(23,74)(24,76)(25,69)(26,71)(27,70)(28,72)(29,65)(30,67)(31,66)(32,68)(33,61)(34,63)(35,62)(36,64)(37,57)(38,59)(39,58)(40,60)(41,53)(42,55)(43,54)(44,56)(45,49)(46,51)(47,50)(48,52);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,89)(10,90)(11,92)(12,91)(13,85)(14,86)(15,88)(16,87)(17,81)(18,82)(19,84)(20,83)(21,77)(22,78)(23,80)(24,79)(25,73)(26,74)(27,76)(28,75)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)(37,61)(38,62)(39,64)(40,63)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(51,52);;
s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79)(81,84)(82,83)(85,88)(86,87)(89,92)(90,91);;
s3 := (93,94);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(94)!( 2, 3)( 5,89)( 6,91)( 7,90)( 8,92)( 9,85)(10,87)(11,86)(12,88)(13,81)(14,83)(15,82)(16,84)(17,77)(18,79)(19,78)(20,80)(21,73)(22,75)(23,74)(24,76)(25,69)(26,71)(27,70)(28,72)(29,65)(30,67)(31,66)(32,68)(33,61)(34,63)(35,62)(36,64)(37,57)(38,59)(39,58)(40,60)(41,53)(42,55)(43,54)(44,56)(45,49)(46,51)(47,50)(48,52);
s1 := Sym(94)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,89)(10,90)(11,92)(12,91)(13,85)(14,86)(15,88)(16,87)(17,81)(18,82)(19,84)(20,83)(21,77)(22,78)(23,80)(24,79)(25,73)(26,74)(27,76)(28,75)(29,69)(30,70)(31,72)(32,71)(33,65)(34,66)(35,68)(36,67)(37,61)(38,62)(39,64)(40,63)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(51,52);
s2 := Sym(94)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79)(81,84)(82,83)(85,88)(86,87)(89,92)(90,91);
s3 := Sym(94)!(93,94);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;