Polytope of Type {6,2,12,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,12,2,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,47319)
Rank : 6
Schlafli Type : {6,2,12,2,3}
Number of vertices, edges, etc : 6, 6, 12, 12, 3, 3
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 : {3,2,12,2,3}*864, {6,2,6,2,3}*864
   3-fold quotients : {2,2,12,2,3}*576, {6,2,4,2,3}*576
   4-fold quotients : {3,2,6,2,3}*432, {6,2,3,2,3}*432
   6-fold quotients : {3,2,4,2,3}*288, {2,2,6,2,3}*288, {6,2,2,2,3}*288
   8-fold quotients : {3,2,3,2,3}*216
   9-fold quotients : {2,2,4,2,3}*192
   12-fold quotients : {2,2,3,2,3}*144, {3,2,2,2,3}*144
   18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope