Polytope of Type {31,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {31,2}*124
if this polytope has a name.
Group : SmallGroup(124,3)
Rank : 3
Schlafli Type : {31,2}
Number of vertices, edges, etc : 31, 31, 2
Order of s₀s₁s₂ : 62
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {31,2,2} of size 248
   {31,2,3} of size 372
   {31,2,4} of size 496
   {31,2,5} of size 620
   {31,2,6} of size 744
   {31,2,7} of size 868
   {31,2,8} of size 992
   {31,2,9} of size 1116
   {31,2,10} of size 1240
   {31,2,11} of size 1364
   {31,2,12} of size 1488
   {31,2,13} of size 1612
   {31,2,14} of size 1736
   {31,2,15} of size 1860
   {31,2,16} of size 1984
Vertex Figure Of :
   {2,31,2} of size 248
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {62,2}*248
   3-fold covers : {93,2}*372
   4-fold covers : {124,2}*496, {62,4}*496
   5-fold covers : {155,2}*620
   6-fold covers : {62,6}*744, {186,2}*744
   7-fold covers : {217,2}*868
   8-fold covers : {124,4}*992, {248,2}*992, {62,8}*992
   9-fold covers : {279,2}*1116, {93,6}*1116
   10-fold covers : {62,10}*1240, {310,2}*1240
   11-fold covers : {341,2}*1364
   12-fold covers : {62,12}*1488, {124,6}*1488a, {372,2}*1488, {186,4}*1488a, {93,6}*1488, {93,4}*1488
   13-fold covers : {403,2}*1612
   14-fold covers : {62,14}*1736, {434,2}*1736
   15-fold covers : {465,2}*1860
   16-fold covers : {124,8}*1984a, {248,4}*1984a, {124,8}*1984b, {248,4}*1984b, {124,4}*1984, {62,16}*1984, {496,2}*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);;
s2 := (32,33);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(33)!( 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(33)!( 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);
s2 := Sym(33)!(32,33);
poly := sub<Sym(33)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope