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# Polytope of Type {6,4,3}

Atlas Canonical Name : {6,4,3}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157478)
Rank : 4
Schlafli Type : {6,4,3}
Number of vertices, edges, etc : 24, 96, 48, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 4
Special Properties :
Orientable
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 : {3,4,3}*576
32-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);;
s1 := ( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,10)(11,12)(13,15)(14,16)(17,18)(19,22)
(20,21)(23,24);;
s2 := ( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);;
s3 := ( 1,10)( 2, 9)( 3,16)( 4,15)( 5,11)( 6,12)( 7,14)( 8,13)(17,18);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s3*s0*s2*s1*s0*s2*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);
s1 := Sym(24)!( 1, 2)( 3, 7)( 4, 8)( 5, 6)( 9,10)(11,12)(13,15)(14,16)(17,18)
(19,22)(20,21)(23,24);
s2 := Sym(24)!( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);
s3 := Sym(24)!( 1,10)( 2, 9)( 3,16)( 4,15)( 5,11)( 6,12)( 7,14)( 8,13)(17,18);
poly := sub<Sym(24)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s3*s0*s2*s1*s0*s2*s1*s3*s2*s3*s1*s2*s0*s1*s3*s2*s3*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope