Polytope of Type {23}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {23}*46
Also Known As : 23-gon, {23}. if this polytope has another name.
Group : SmallGroup(46,1)
Rank : 2
Schlafli Type : {23}
Number of vertices, edges, etc : 23, 23
Order of s₀s₁ : 23
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {23,2} of size 92
Vertex Figure Of :
   {2,23} of size 92
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {46}*92
   3-fold covers : {69}*138
   4-fold covers : {92}*184
   5-fold covers : {115}*230
   6-fold covers : {138}*276
   7-fold covers : {161}*322
   8-fold covers : {184}*368
   9-fold covers : {207}*414
   10-fold covers : {230}*460
   11-fold covers : {253}*506
   12-fold covers : {276}*552
   13-fold covers : {299}*598
   14-fold covers : {322}*644
   15-fold covers : {345}*690
   16-fold covers : {368}*736
   17-fold covers : {391}*782
   18-fold covers : {414}*828
   19-fold covers : {437}*874
   20-fold covers : {460}*920
   21-fold covers : {483}*966
   22-fold covers : {506}*1012
   23-fold covers : {529}*1058
   24-fold covers : {552}*1104
   25-fold covers : {575}*1150
   26-fold covers : {598}*1196
   27-fold covers : {621}*1242
   28-fold covers : {644}*1288
   29-fold covers : {667}*1334
   30-fold covers : {690}*1380
   31-fold covers : {713}*1426
   32-fold covers : {736}*1472
   33-fold covers : {759}*1518
   34-fold covers : {782}*1564
   35-fold covers : {805}*1610
   36-fold covers : {828}*1656
   37-fold covers : {851}*1702
   38-fold covers : {874}*1748
   39-fold covers : {897}*1794
   40-fold covers : {920}*1840
   41-fold covers : {943}*1886
   42-fold covers : {966}*1932
   43-fold covers : {989}*1978
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(23)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23);
s1 := Sym(23)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22);
poly := sub<Sym(23)|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 >;

References : None.
to this polytope