Questions?
See the FAQ
or other info.

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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,3,6,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46165)
Rank : 7
Schlafli Type : {2,2,2,3,6,6}
Number of vertices, edges, etc : 2, 2, 2, 3, 9, 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) :
   2-fold quotients : {2,2,2,3,6,3}*864
   3-fold quotients : {2,2,2,3,2,6}*576
   6-fold quotients : {2,2,2,3,2,3}*288
   9-fold quotients : {2,2,2,3,2,2}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24);;
s4 := ( 8, 9)(10,11)(13,15)(17,18)(19,20)(22,24);;
s5 := ( 7,10)( 8,12)( 9,11)(14,15)(16,19)(17,21)(18,20)(23,24);;
s6 := ( 7,16)( 8,18)( 9,17)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20);;
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*s1*s0*s1, 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, 
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, 
s3*s4*s3*s4*s3*s4, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s6*s4*s5*s4*s5*s6*s4*s5*s4*s5, s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!(5,6);
s3 := Sym(24)!( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24);
s4 := Sym(24)!( 8, 9)(10,11)(13,15)(17,18)(19,20)(22,24);
s5 := Sym(24)!( 7,10)( 8,12)( 9,11)(14,15)(16,19)(17,21)(18,20)(23,24);
s6 := Sym(24)!( 7,16)( 8,18)( 9,17)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20);
poly := sub<Sym(24)|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*s1*s0*s1, 
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, 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, s3*s4*s3*s4*s3*s4, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s6*s4*s5*s4*s5*s6*s4*s5*s4*s5, 
s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 >; 
 

to this polytope