Polytope of Type {2,29}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,29}*116
if this polytope has a name.
Group : SmallGroup(116,4)
Rank : 3
Schlafli Type : {2,29}
Number of vertices, edges, etc : 2, 29, 29
Order of s₀s₁s₂ : 58
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,29,2} of size 232
Vertex Figure Of :
   {2,2,29} of size 232
   {3,2,29} of size 348
   {4,2,29} of size 464
   {5,2,29} of size 580
   {6,2,29} of size 696
   {7,2,29} of size 812
   {8,2,29} of size 928
   {9,2,29} of size 1044
   {10,2,29} of size 1160
   {11,2,29} of size 1276
   {12,2,29} of size 1392
   {13,2,29} of size 1508
   {14,2,29} of size 1624
   {15,2,29} of size 1740
   {16,2,29} of size 1856
   {17,2,29} of size 1972
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,58}*232
   3-fold covers : {2,87}*348
   4-fold covers : {2,116}*464, {4,58}*464
   5-fold covers : {2,145}*580
   6-fold covers : {6,58}*696, {2,174}*696
   7-fold covers : {2,203}*812
   8-fold covers : {4,116}*928, {2,232}*928, {8,58}*928
   9-fold covers : {2,261}*1044, {6,87}*1044
   10-fold covers : {10,58}*1160, {2,290}*1160
   11-fold covers : {2,319}*1276
   12-fold covers : {12,58}*1392, {6,116}*1392a, {2,348}*1392, {4,174}*1392a, {6,87}*1392, {4,87}*1392
   13-fold covers : {2,377}*1508
   14-fold covers : {14,58}*1624, {2,406}*1624
   15-fold covers : {2,435}*1740
   16-fold covers : {8,116}*1856a, {4,232}*1856a, {8,116}*1856b, {4,232}*1856b, {4,116}*1856, {16,58}*1856, {2,464}*1856
   17-fold covers : {2,493}*1972
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);;
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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope