Polytope of Type {31}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {31}*62
Also Known As : 31-gon, {31}. if this polytope has another name.
Group : SmallGroup(62,1)
Rank : 2
Schlafli Type : {31}
Number of vertices, edges, etc : 31, 31
Order of s₀s₁ : 31
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {31,2} of size 124
Vertex Figure Of :
   {2,31} of size 124
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {62}*124
   3-fold covers : {93}*186
   4-fold covers : {124}*248
   5-fold covers : {155}*310
   6-fold covers : {186}*372
   7-fold covers : {217}*434
   8-fold covers : {248}*496
   9-fold covers : {279}*558
   10-fold covers : {310}*620
   11-fold covers : {341}*682
   12-fold covers : {372}*744
   13-fold covers : {403}*806
   14-fold covers : {434}*868
   15-fold covers : {465}*930
   16-fold covers : {496}*992
   17-fold covers : {527}*1054
   18-fold covers : {558}*1116
   19-fold covers : {589}*1178
   20-fold covers : {620}*1240
   21-fold covers : {651}*1302
   22-fold covers : {682}*1364
   23-fold covers : {713}*1426
   24-fold covers : {744}*1488
   25-fold covers : {775}*1550
   26-fold covers : {806}*1612
   27-fold covers : {837}*1674
   28-fold covers : {868}*1736
   29-fold covers : {899}*1798
   30-fold covers : {930}*1860
   31-fold covers : {961}*1922
   32-fold covers : {992}*1984
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)(24,25)(26,27)(28,29)(30,31);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);
s1 := Sym(31)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);
poly := sub<Sym(31)|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 >;

References : None.
to this polytope