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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,2,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,47915)
Rank : 7
Schlafli Type : {3,2,2,2,6,6}
Number of vertices, edges, etc : 3, 3, 2, 2, 6, 18, 6
Order of s₀s₁s₂s₃s₄s₅s₆ : 6
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 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) :
   3-fold quotients : {3,2,2,2,2,6}*576, {3,2,2,2,6,2}*576
   6-fold quotients : {3,2,2,2,2,3}*288, {3,2,2,2,3,2}*288
   9-fold quotients : {3,2,2,2,2,2}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (6,7);;
s4 := (12,13)(16,17)(18,19)(20,21)(22,23)(24,25);;
s5 := ( 8,12)( 9,16)(10,20)(11,18)(14,24)(15,22)(19,21)(23,25);;
s6 := ( 8,14)( 9,10)(11,15)(12,22)(13,23)(16,18)(17,19)(20,24)(21,25);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s2*s0*s2, s1*s2*s1*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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s0*s1*s0*s1*s0*s1, s4*s5*s6*s5*s4*s5*s6*s5, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(25)!(2,3);
s1 := Sym(25)!(1,2);
s2 := Sym(25)!(4,5);
s3 := Sym(25)!(6,7);
s4 := Sym(25)!(12,13)(16,17)(18,19)(20,21)(22,23)(24,25);
s5 := Sym(25)!( 8,12)( 9,16)(10,20)(11,18)(14,24)(15,22)(19,21)(23,25);
s6 := Sym(25)!( 8,14)( 9,10)(11,15)(12,22)(13,23)(16,18)(17,19)(20,24)(21,25);
poly := sub<Sym(25)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*s2, 
s1*s2*s1*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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s0*s1*s0*s1*s0*s1, 
s4*s5*s6*s5*s4*s5*s6*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 >;

to this polytope