Polytope of Type {11,2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,6,6}*1584a
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 5
Schlafli Type : {11,2,6,6}
Number of vertices, edges, etc : 11, 11, 6, 18, 6
Order of s₀s₁s₂s₃s₄ : 66
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {11,2,2,6}*528, {11,2,6,2}*528
   6-fold quotients : {11,2,2,3}*264, {11,2,3,2}*264
   9-fold quotients : {11,2,2,2}*176
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := (16,17)(20,21)(22,23)(24,25)(26,27)(28,29);;
s3 := (12,16)(13,20)(14,24)(15,22)(18,28)(19,26)(23,25)(27,29);;
s4 := (12,18)(13,14)(15,19)(16,26)(17,27)(20,22)(21,23)(24,28)(25,29);;
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(29)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(29)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(29)!(16,17)(20,21)(22,23)(24,25)(26,27)(28,29);
s3 := Sym(29)!(12,16)(13,20)(14,24)(15,22)(18,28)(19,26)(23,25)(27,29);
s4 := Sym(29)!(12,18)(13,14)(15,19)(16,26)(17,27)(20,22)(21,23)(24,28)(25,29);
poly := sub<Sym(29)|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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope