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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,11,2,2}*352
if this polytope has a name.
Group : SmallGroup(352,194)
Rank : 6
Schlafli Type : {2,2,11,2,2}
Number of vertices, edges, etc : 2, 2, 11, 11, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 22
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,11,2,2,2} of size 704
   {2,2,11,2,2,3} of size 1056
   {2,2,11,2,2,4} of size 1408
   {2,2,11,2,2,5} of size 1760
Vertex Figure Of :
   {2,2,2,11,2,2} of size 704
   {3,2,2,11,2,2} of size 1056
   {4,2,2,11,2,2} of size 1408
   {5,2,2,11,2,2} of size 1760
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,11,2,4}*704, {4,2,11,2,2}*704, {2,2,22,2,2}*704
   3-fold covers : {2,2,11,2,6}*1056, {6,2,11,2,2}*1056, {2,2,33,2,2}*1056
   4-fold covers : {4,2,11,2,4}*1408, {2,2,11,2,8}*1408, {8,2,11,2,2}*1408, {2,2,22,2,4}*1408, {2,2,22,4,2}*1408, {2,4,22,2,2}*1408, {4,2,22,2,2}*1408, {2,2,44,2,2}*1408
   5-fold covers : {2,2,11,2,10}*1760, {10,2,11,2,2}*1760, {2,2,55,2,2}*1760
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s4 := (16,17);;
s5 := (18,19);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, 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(19)!(1,2);
s1 := Sym(19)!(3,4);
s2 := Sym(19)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s3 := Sym(19)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s4 := Sym(19)!(16,17);
s5 := Sym(19)!(18,19);
poly := sub<Sym(19)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
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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