Polytope of Type {5,2,11}

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

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s3 := ( 6, 7)( 8, 9)(10,11)(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, 
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(16)!(2,3)(4,5);
s1 := Sym(16)!(1,2)(3,4);
s2 := Sym(16)!( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s3 := Sym(16)!( 6, 7)( 8, 9)(10,11)(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, 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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