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Polytope of Type {3,2,11,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,11,2}*264
if this polytope has a name.
Group : SmallGroup(264,34)
Rank : 5
Schlafli Type : {3,2,11,2}
Number of vertices, edges, etc : 3, 3, 11, 11, 2
Order of s0s1s2s3s4 : 66
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,11,2,2} of size 528
   {3,2,11,2,3} of size 792
   {3,2,11,2,4} of size 1056
   {3,2,11,2,5} of size 1320
   {3,2,11,2,6} of size 1584
   {3,2,11,2,7} of size 1848
Vertex Figure Of :
   {2,3,2,11,2} of size 528
   {3,3,2,11,2} of size 1056
   {4,3,2,11,2} of size 1056
   {6,3,2,11,2} of size 1584
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,22,2}*528, {6,2,11,2}*528
   3-fold covers : {9,2,11,2}*792, {3,2,33,2}*792
   4-fold covers : {12,2,11,2}*1056, {3,2,44,2}*1056, {3,2,22,4}*1056, {6,2,22,2}*1056
   5-fold covers : {15,2,11,2}*1320, {3,2,55,2}*1320
   6-fold covers : {9,2,22,2}*1584, {18,2,11,2}*1584, {3,2,22,6}*1584, {3,6,22,2}*1584, {3,2,66,2}*1584, {6,2,33,2}*1584
   7-fold covers : {21,2,11,2}*1848, {3,2,77,2}*1848
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s4 := (15,16);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(16)!(2,3);
s1 := Sym(16)!(1,2);
s2 := Sym(16)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s3 := Sym(16)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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