Part of the Atlas of Small Regular Polytopes

Polytope of Type {96,2,2}

Atlas Canonical Name {96,2,2}*768

Overview

Group
SmallGroup(768,327684)
Rank
4
Schläfli Type
{96,2,2}
Vertices, edges, …
96, 96, 2, 2
Order of s0s1s2s3
96
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83)(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)(69,86)(70,88)(71,90)(72,89);;
s1 := ( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)(10,56)(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)(21,63)(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)(32,94)(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)(43,83)(44,82)(45,84)(46,80)(47,79)(48,81);;
s2 := (97,98);;
s3 := ( 99,100);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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(100)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)(35,45)(36,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,82)(56,84)(57,83)(58,79)(59,81)(60,80)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)(69,86)(70,88)(71,90)(72,89);
s1 := Sym(100)!( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,58)( 9,60)(10,56)(11,55)(12,57)(13,68)(14,67)(15,69)(16,71)(17,70)(18,72)(19,62)(20,61)(21,63)(22,65)(23,64)(24,66)(25,86)(26,85)(27,87)(28,89)(29,88)(30,90)(31,95)(32,94)(33,96)(34,92)(35,91)(36,93)(37,74)(38,73)(39,75)(40,77)(41,76)(42,78)(43,83)(44,82)(45,84)(46,80)(47,79)(48,81);
s2 := Sym(100)!(97,98);
s3 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*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 >;