Polytope of Type {23,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {23,2}*92
if this polytope has a name.
Group : SmallGroup(92,3)
Rank : 3
Schlafli Type : {23,2}
Number of vertices, edges, etc : 23, 23, 2
Order of s₀s₁s₂ : 46
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {23,2,2} of size 184
   {23,2,3} of size 276
   {23,2,4} of size 368
   {23,2,5} of size 460
   {23,2,6} of size 552
   {23,2,7} of size 644
   {23,2,8} of size 736
   {23,2,9} of size 828
   {23,2,10} of size 920
   {23,2,11} of size 1012
   {23,2,12} of size 1104
   {23,2,13} of size 1196
   {23,2,14} of size 1288
   {23,2,15} of size 1380
   {23,2,16} of size 1472
   {23,2,17} of size 1564
   {23,2,18} of size 1656
   {23,2,19} of size 1748
   {23,2,20} of size 1840
   {23,2,21} of size 1932
Vertex Figure Of :
   {2,23,2} of size 184
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {46,2}*184
   3-fold covers : {69,2}*276
   4-fold covers : {92,2}*368, {46,4}*368
   5-fold covers : {115,2}*460
   6-fold covers : {46,6}*552, {138,2}*552
   7-fold covers : {161,2}*644
   8-fold covers : {92,4}*736, {184,2}*736, {46,8}*736
   9-fold covers : {207,2}*828, {69,6}*828
   10-fold covers : {46,10}*920, {230,2}*920
   11-fold covers : {253,2}*1012
   12-fold covers : {46,12}*1104, {92,6}*1104a, {276,2}*1104, {138,4}*1104a, {69,6}*1104, {69,4}*1104
   13-fold covers : {299,2}*1196
   14-fold covers : {46,14}*1288, {322,2}*1288
   15-fold covers : {345,2}*1380
   16-fold covers : {92,8}*1472a, {184,4}*1472a, {92,8}*1472b, {184,4}*1472b, {92,4}*1472, {46,16}*1472, {368,2}*1472
   17-fold covers : {391,2}*1564
   18-fold covers : {46,18}*1656, {414,2}*1656, {138,6}*1656a, {138,6}*1656b, {138,6}*1656c
   19-fold covers : {437,2}*1748
   20-fold covers : {46,20}*1840, {92,10}*1840, {460,2}*1840, {230,4}*1840
   21-fold covers : {483,2}*1932
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);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);;
s2 := (24,25);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23);
s1 := Sym(25)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22);
s2 := Sym(25)!(24,25);
poly := sub<Sym(25)|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 >;

to this polytope