Part of the Atlas of Small Regular Polytopes

Polytope of Type {96}

Atlas Canonical Name {96}*192

Overview

Group
SmallGroup(192,7)
Rank
2
Schläfli Type
{96}
Vertices, edges, …
96, 96
Order of s0s1
96
Also known as
96-gon, {96}. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Locally Spherical
  • Orientable
  • Self-Dual

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

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Irregular Quotients of which this is a minimal cover

None.

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);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(96)!( 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(96)!( 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);
poly := sub<Sym(96)|s0,s1>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.