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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,2}*864c
if this polytope has a name.
Group : SmallGroup(864,4033)
Rank : 5
Schlafli Type : {2,6,6,2}
Number of vertices, edges, etc : 2, 18, 54, 18, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2,2} of size 1728
Vertex Figure Of :
   {2,2,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,6,2}*432
   3-fold quotients : {2,6,6,2}*288c
   6-fold quotients : {2,3,6,2}*144
   9-fold quotients : {2,6,2,2}*96
   18-fold quotients : {2,3,2,2}*48
   27-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,6,2}*1728a, {4,6,6,2}*1728a, {2,6,6,4}*1728c, {2,6,12,2}*1728c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 9)( 4,10)( 5,11)(12,18)(13,19)(14,20);;
s2 := ( 3,12)( 4,13)( 5,14)( 6,19)( 7,20)( 8,18)( 9,17)(10,15)(11,16);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);;
s4 := (21,22);;
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*s1*s0*s1, 
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 3, 9)( 4,10)( 5,11)(12,18)(13,19)(14,20);
s2 := Sym(22)!( 3,12)( 4,13)( 5,14)( 6,19)( 7,20)( 8,18)( 9,17)(10,15)(11,16);
s3 := Sym(22)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);
s4 := Sym(22)!(21,22);
poly := sub<Sym(22)|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*s1*s0*s1, s0*s2*s0*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

to this polytope