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

Atlas Canonical Name : {3,2,3,6,3}*648
if this polytope has a name.
Group : SmallGroup(648,555)
Rank : 6
Schlafli Type : {3,2,3,6,3}
Number of vertices, edges, etc : 3, 3, 3, 9, 9, 3
Order of s0s1s2s3s4s5 : 3
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,3,6,3,2} of size 1296
Vertex Figure Of :
{2,3,2,3,6,3} of size 1296
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,2,3,2,3}*216
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,3,6,6}*1296a, {3,2,6,6,3}*1296a, {6,2,3,6,3}*1296
3-fold covers : {3,2,3,6,9}*1944, {3,2,9,6,3}*1944, {9,2,3,6,3}*1944, {3,6,3,6,3}*1944, {3,2,3,6,3}*1944a, {3,2,3,6,3}*1944b
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7, 8)( 9,10)(11,12);;
s3 := ( 5, 7)( 6, 9)(11,12);;
s4 := ( 4, 5)( 7,12)( 8,11)( 9,10);;
s5 := ( 5, 6)( 7, 9)( 8,10)(11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2);
s2 := Sym(12)!( 7, 8)( 9,10)(11,12);
s3 := Sym(12)!( 5, 7)( 6, 9)(11,12);
s4 := Sym(12)!( 4, 5)( 7,12)( 8,11)( 9,10);
s5 := Sym(12)!( 5, 6)( 7, 9)( 8,10)(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 >;

```

to this polytope