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Polytope of Type {11,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,5}*220
if this polytope has a name.
Group : SmallGroup(220,11)
Rank : 4
Schlafli Type : {11,2,5}
Number of vertices, edges, etc : 11, 11, 5, 5
Order of s0s1s2s3 : 55
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2,5,2} of size 440
   {11,2,5,3} of size 1320
   {11,2,5,5} of size 1320
Vertex Figure Of :
   {2,11,2,5} of size 440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {11,2,10}*440, {22,2,5}*440
   3-fold covers : {11,2,15}*660, {33,2,5}*660
   4-fold covers : {11,2,20}*880, {44,2,5}*880, {22,2,10}*880
   5-fold covers : {11,2,25}*1100, {55,2,5}*1100
   6-fold covers : {11,2,30}*1320, {22,2,15}*1320, {33,2,10}*1320, {66,2,5}*1320
   7-fold covers : {11,2,35}*1540, {77,2,5}*1540
   8-fold covers : {11,2,40}*1760, {88,2,5}*1760, {22,2,20}*1760, {44,2,10}*1760, {22,4,10}*1760
   9-fold covers : {11,2,45}*1980, {99,2,5}*1980, {33,2,15}*1980
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);;
s3 := (12,13)(14,15);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(16)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(16)!(13,14)(15,16);
s3 := Sym(16)!(12,13)(14,15);
poly := sub<Sym(16)|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*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 >; 
 

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