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# Polytope of Type {4,6,3}

Atlas Canonical Name : {4,6,3}*576b
if this polytope has a name.
Group : SmallGroup(576,8654)
Rank : 4
Schlafli Type : {4,6,3}
Number of vertices, edges, etc : 16, 48, 36, 3
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,3,2} of size 1152
Vertex Figure Of :
{2,4,6,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,3}*1152c, {4,6,6}*1152i
3-fold covers : {4,6,9}*1728b, {4,6,3}*1728b
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 4)( 5, 8)( 6, 7)( 9,11)(10,12);;
s1 := ( 2, 3)( 7, 8)(10,12);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);;
s3 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3 ];;
poly := F / rels;;

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

```
References : None.
to this polytope