Polytope of Type {2,31}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,31}*124
if this polytope has a name.
Group : SmallGroup(124,3)
Rank : 3
Schlafli Type : {2,31}
Number of vertices, edges, etc : 2, 31, 31
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 :
   {2,31,2} of size 248
Vertex Figure Of :
   {2,2,31} of size 248
   {3,2,31} of size 372
   {4,2,31} of size 496
   {5,2,31} of size 620
   {6,2,31} of size 744
   {7,2,31} of size 868
   {8,2,31} of size 992
   {9,2,31} of size 1116
   {10,2,31} of size 1240
   {11,2,31} of size 1364
   {12,2,31} of size 1488
   {13,2,31} of size 1612
   {14,2,31} of size 1736
   {15,2,31} of size 1860
   {16,2,31} of size 1984
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,62}*248
   3-fold covers : {2,93}*372
   4-fold covers : {2,124}*496, {4,62}*496
   5-fold covers : {2,155}*620
   6-fold covers : {6,62}*744, {2,186}*744
   7-fold covers : {2,217}*868
   8-fold covers : {4,124}*992, {2,248}*992, {8,62}*992
   9-fold covers : {2,279}*1116, {6,93}*1116
   10-fold covers : {10,62}*1240, {2,310}*1240
   11-fold covers : {2,341}*1364
   12-fold covers : {12,62}*1488, {6,124}*1488a, {2,372}*1488, {4,186}*1488a, {6,93}*1488, {4,93}*1488
   13-fold covers : {2,403}*1612
   14-fold covers : {14,62}*1736, {2,434}*1736
   15-fold covers : {2,465}*1860
   16-fold covers : {8,124}*1984a, {4,248}*1984a, {8,124}*1984b, {4,248}*1984b, {4,124}*1984, {16,62}*1984, {2,496}*1984
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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)(32,33);;
s2 := ( 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)(31,32);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(33)!(1,2);
s1 := Sym(33)!( 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)(32,33);
s2 := Sym(33)!( 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)(31,32);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope