Polytope of Type {29,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {29,2}*116
if this polytope has a name.
Group : SmallGroup(116,4)
Rank : 3
Schlafli Type : {29,2}
Number of vertices, edges, etc : 29, 29, 2
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 :
   {29,2,2} of size 232
   {29,2,3} of size 348
   {29,2,4} of size 464
   {29,2,5} of size 580
   {29,2,6} of size 696
   {29,2,7} of size 812
   {29,2,8} of size 928
   {29,2,9} of size 1044
   {29,2,10} of size 1160
   {29,2,11} of size 1276
   {29,2,12} of size 1392
   {29,2,13} of size 1508
   {29,2,14} of size 1624
   {29,2,15} of size 1740
   {29,2,16} of size 1856
   {29,2,17} of size 1972
Vertex Figure Of :
   {2,29,2} of size 232
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {58,2}*232
   3-fold covers : {87,2}*348
   4-fold covers : {116,2}*464, {58,4}*464
   5-fold covers : {145,2}*580
   6-fold covers : {58,6}*696, {174,2}*696
   7-fold covers : {203,2}*812
   8-fold covers : {116,4}*928, {232,2}*928, {58,8}*928
   9-fold covers : {261,2}*1044, {87,6}*1044
   10-fold covers : {58,10}*1160, {290,2}*1160
   11-fold covers : {319,2}*1276
   12-fold covers : {58,12}*1392, {116,6}*1392a, {348,2}*1392, {174,4}*1392a, {87,6}*1392, {87,4}*1392
   13-fold covers : {377,2}*1508
   14-fold covers : {58,14}*1624, {406,2}*1624
   15-fold covers : {435,2}*1740
   16-fold covers : {116,8}*1856a, {232,4}*1856a, {116,8}*1856b, {232,4}*1856b, {116,4}*1856, {58,16}*1856, {464,2}*1856
   17-fold covers : {493,2}*1972
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);;
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);;
s2 := (30,31);;
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 ];;
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);
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);
s2 := Sym(31)!(30,31);
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*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 >;

to this polytope