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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,3,2}*648b
if this polytope has a name.
Group : SmallGroup(648,299)
Rank : 5
Schlafli Type : {3,6,3,2}
Number of vertices, edges, etc : 9, 27, 27, 3, 2
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,6,3,2,2} of size 1296
{3,6,3,2,3} of size 1944
Vertex Figure Of :
{2,3,6,3,2} of size 1296
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,6,3,2}*216
9-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,6,6,2}*1296a, {6,6,3,2}*1296a
3-fold covers : {3,6,3,2}*1944, {9,6,3,2}*1944a, {3,6,9,2}*1944b, {3,6,3,6}*1944b
Permutation Representation (GAP) :
```s0 := (1,7)(2,8)(3,9);;
s1 := (4,7)(5,8)(6,9);;
s2 := (2,3)(4,5)(8,9);;
s3 := (2,3)(5,6)(8,9);;
s4 := (10,11);;
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,
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*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(1,7)(2,8)(3,9);
s1 := Sym(11)!(4,7)(5,8)(6,9);
s2 := Sym(11)!(2,3)(4,5)(8,9);
s3 := Sym(11)!(2,3)(5,6)(8,9);
s4 := Sym(11)!(10,11);
poly := sub<Sym(11)|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, 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*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

```

to this polytope