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Polytope of Type {11,2,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,11}*484
if this polytope has a name.
Group : SmallGroup(484,9)
Rank : 4
Schlafli Type : {11,2,11}
Number of vertices, edges, etc : 11, 11, 11, 11
Order of s0s1s2s3 : 11
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2,11,2} of size 968
Vertex Figure Of :
   {2,11,2,11} of size 968
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {11,2,22}*968, {22,2,11}*968
   3-fold covers : {11,2,33}*1452, {33,2,11}*1452
   4-fold covers : {11,2,44}*1936, {44,2,11}*1936, {22,2,22}*1936
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (13,14)(15,16)(17,18)(19,20)(21,22);;
s3 := (12,13)(14,15)(16,17)(18,19)(20,21);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(22)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(22)!(13,14)(15,16)(17,18)(19,20)(21,22);
s3 := Sym(22)!(12,13)(14,15)(16,17)(18,19)(20,21);
poly := sub<Sym(22)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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