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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,3,12}*1728
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {6,2,3,12}
Number of vertices, edges, etc : 6, 6, 6, 36, 24
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,2,3,12}*864
   3-fold quotients : {2,2,3,12}*576, {6,2,3,4}*576
   4-fold quotients : {6,2,3,6}*432
   6-fold quotients : {3,2,3,4}*288, {6,2,3,4}*288
   8-fold quotients : {3,2,3,6}*216
   9-fold quotients : {2,2,3,4}*192
   12-fold quotients : {3,2,3,4}*144, {2,2,3,6}*144, {6,2,3,2}*144
   18-fold quotients : {2,2,3,4}*96
   24-fold quotients : {3,2,3,2}*72
   36-fold quotients : {2,2,3,2}*48
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 := ( 9,10)(11,15)(12,16)(13,18)(14,17);;
s3 := ( 7,11)( 8,13)( 9,12)(10,14)(16,17);;
s4 := ( 7, 8)( 9,10)(11,16)(12,15)(13,18)(14,17);;
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, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope