Polytope of Type {2,2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,12}*864b
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 5
Schlafli Type : {2,2,6,12}
Number of vertices, edges, etc : 2, 2, 9, 54, 18
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,12,2} of size 1728
Vertex Figure Of :
   {2,2,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,6,4}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,6,12}*1728b, {2,2,6,12}*1728f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope