Polytope of Type {4,2,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,3}*864
if this polytope has a name.
Group : SmallGroup(864,2470)
Rank : 5
Schlafli Type : {4,2,6,3}
Number of vertices, edges, etc : 4, 4, 18, 27, 9
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,6,3,2} of size 1728
Vertex Figure Of :
   {2,4,2,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,6,3}*432
   3-fold quotients : {4,2,6,3}*288
   6-fold quotients : {2,2,6,3}*144
   9-fold quotients : {4,2,2,3}*96
   18-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,6,3}*1728, {4,4,6,3}*1728a, {4,2,6,6}*1728a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!( 8, 9)(10,11)(12,13);
s3 := Sym(13)!( 6,10)( 7, 8)( 9,11);
s4 := Sym(13)!( 5, 6)( 8,12)( 9,13);
poly := sub<Sym(13)|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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3 >;

to this polytope