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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,3,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,47341)
Rank : 6
Schlafli Type : {4,6,2,3,6}
Number of vertices, edges, etc : 4, 12, 6, 3, 9, 6
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,6,2,3,6}*864
   3-fold quotients : {4,2,2,3,6}*576, {4,6,2,3,2}*576a
   4-fold quotients : {2,3,2,3,6}*432
   6-fold quotients : {2,2,2,3,6}*288, {2,6,2,3,2}*288
   9-fold quotients : {4,2,2,3,2}*192
   12-fold quotients : {2,3,2,3,2}*144
   18-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 5)( 6, 9)( 7,10);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);;
s2 := ( 1, 3)( 2, 6)( 5, 9)( 8,11);;
s3 := (14,15)(16,17)(18,21)(19,20);;
s4 := (13,18)(14,16)(15,20)(17,19);;
s5 := (16,17)(18,19)(20,21);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!( 2, 5)( 6, 9)( 7,10);
s1 := Sym(21)!( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);
s2 := Sym(21)!( 1, 3)( 2, 6)( 5, 9)( 8,11);
s3 := Sym(21)!(14,15)(16,17)(18,21)(19,20);
s4 := Sym(21)!(13,18)(14,16)(15,20)(17,19);
s5 := Sym(21)!(16,17)(18,19)(20,21);
poly := sub<Sym(21)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope