Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,90,2}

Atlas Canonical Name {2,90,2}*720

Overview

Group
SmallGroup(720,407)
Rank
4
Schläfli Type
{2,90,2}
Vertices, edges, …
2, 90, 90, 2
Order of s0s1s2s3
90
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat
  • Self-Dual

Quotients maximal quotients in bold

2-fold

3-fold

5-fold

6-fold

9-fold

10-fold

15-fold

18-fold

30-fold

45-fold

Covers minimal covers in bold

2-fold

Representations

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