Polytope of Type {23,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {23,2,2}*184
if this polytope has a name.
Group : SmallGroup(184,11)
Rank : 4
Schlafli Type : {23,2,2}
Number of vertices, edges, etc : 23, 23, 2, 2
Order of s₀s₁s₂s₃ : 46
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {23,2,2,2} of size 368
   {23,2,2,3} of size 552
   {23,2,2,4} of size 736
   {23,2,2,5} of size 920
   {23,2,2,6} of size 1104
   {23,2,2,7} of size 1288
   {23,2,2,8} of size 1472
   {23,2,2,9} of size 1656
   {23,2,2,10} of size 1840
Vertex Figure Of :
   {2,23,2,2} of size 368
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {23,2,4}*368, {46,2,2}*368
   3-fold covers : {23,2,6}*552, {69,2,2}*552
   4-fold covers : {23,2,8}*736, {92,2,2}*736, {46,2,4}*736, {46,4,2}*736
   5-fold covers : {23,2,10}*920, {115,2,2}*920
   6-fold covers : {23,2,12}*1104, {69,2,4}*1104, {46,2,6}*1104, {46,6,2}*1104, {138,2,2}*1104
   7-fold covers : {23,2,14}*1288, {161,2,2}*1288
   8-fold covers : {23,2,16}*1472, {46,4,4}*1472, {92,4,2}*1472, {92,2,4}*1472, {46,2,8}*1472, {46,8,2}*1472, {184,2,2}*1472
   9-fold covers : {23,2,18}*1656, {207,2,2}*1656, {69,2,6}*1656, {69,6,2}*1656
   10-fold covers : {23,2,20}*1840, {115,2,4}*1840, {46,2,10}*1840, {46,10,2}*1840, {230,2,2}*1840
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);;
s3 := (26,27);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(27)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23);
s1 := Sym(27)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22);
s2 := Sym(27)!(24,25);
s3 := Sym(27)!(26,27);
poly := sub<Sym(27)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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