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Polytope of Type {23,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {23,2,3}*276
if this polytope has a name.
Group : SmallGroup(276,5)
Rank : 4
Schlafli Type : {23,2,3}
Number of vertices, edges, etc : 23, 23, 3, 3
Order of s0s1s2s3 : 69
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {23,2,3,2} of size 552
   {23,2,3,3} of size 1104
   {23,2,3,4} of size 1104
   {23,2,3,6} of size 1656
Vertex Figure Of :
   {2,23,2,3} of size 552
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {23,2,6}*552, {46,2,3}*552
   3-fold covers : {23,2,9}*828, {69,2,3}*828
   4-fold covers : {23,2,12}*1104, {92,2,3}*1104, {46,2,6}*1104
   5-fold covers : {23,2,15}*1380, {115,2,3}*1380
   6-fold covers : {23,2,18}*1656, {46,2,9}*1656, {46,6,3}*1656, {69,2,6}*1656, {138,2,3}*1656
   7-fold covers : {23,2,21}*1932, {161,2,3}*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 := (25,26);;
s3 := (24,25);;
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*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(26)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23);
s1 := Sym(26)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22);
s2 := Sym(26)!(25,26);
s3 := Sym(26)!(24,25);
poly := sub<Sym(26)|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*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 >; 
 

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