Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,92,2}

Atlas Canonical Name {2,92,2}*736

Overview

Group
SmallGroup(736,175)
Rank
4
Schläfli Type
{2,92,2}
Vertices, edges, …
2, 92, 92, 2
Order of s0s1s2s3
92
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

4-fold

23-fold

46-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(49,72)(50,94)(51,93)(52,92)(53,91)(54,90)(55,89)(56,88)(57,87)(58,86)(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73);;
s2 := ( 3,50)( 4,49)( 5,71)( 6,70)( 7,69)( 8,68)( 9,67)(10,66)(11,65)(12,64)(13,63)(14,62)(15,61)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,52)(25,51)(26,73)(27,72)(28,94)(29,93)(30,92)(31,91)(32,90)(33,89)(34,88)(35,87)(36,86)(37,85)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76)(47,75)(48,74);;
s3 := (95,96);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(96)!(1,2);
s1 := Sym(96)!( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(49,72)(50,94)(51,93)(52,92)(53,91)(54,90)(55,89)(56,88)(57,87)(58,86)(59,85)(60,84)(61,83)(62,82)(63,81)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73);
s2 := Sym(96)!( 3,50)( 4,49)( 5,71)( 6,70)( 7,69)( 8,68)( 9,67)(10,66)(11,65)(12,64)(13,63)(14,62)(15,61)(16,60)(17,59)(18,58)(19,57)(20,56)(21,55)(22,54)(23,53)(24,52)(25,51)(26,73)(27,72)(28,94)(29,93)(30,92)(31,91)(32,90)(33,89)(34,88)(35,87)(36,86)(37,85)(38,84)(39,83)(40,82)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76)(47,75)(48,74);
s3 := Sym(96)!(95,96);
poly := sub<Sym(96)|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*s1*s2*s1*s2 >;