Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,69,2}

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

Overview

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