Polytope of Type {3,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,6}*480
if this polytope has a name.
Group : SmallGroup(480,1186)
Rank : 4
Schlafli Type : {3,6,6}
Number of vertices, edges, etc : 5, 20, 40, 10
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 6
Special Properties :
   Universal
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,6,2} of size 960
   {3,6,6,4} of size 1920
Vertex Figure Of :
   {2,3,6,6} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,3,6}*240, {3,6,3}*240
   4-fold quotients : {3,3,3}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,6}*960, {3,6,12}*960, {6,6,6}*960
   3-fold covers : {3,6,6}*1440a, {3,6,6}*1440b, {3,6,6}*1440c
   4-fold covers : {3,6,24}*1920, {6,6,12}*1920, {6,12,6}*1920a, {12,6,6}*1920, {3,12,12}*1920, {6,12,6}*1920b
Permutation Representation (GAP) :

s0 := (3,5);;
s1 := (4,5);;
s2 := (2,4)(6,7)(8,9);;
s3 := (1,2)(6,8)(7,9);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(9)!(3,5);
s1 := Sym(9)!(4,5);
s2 := Sym(9)!(2,4)(6,7)(8,9);
s3 := Sym(9)!(1,2)(6,8)(7,9);
poly := sub<Sym(9)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope