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

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

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

Permutation Representation (Magma) :

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

to this polytope