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# Polytope of Type {12,6}

Atlas Canonical Name : {12,6}*1152h
if this polytope has a name.
Group : SmallGroup(1152,157478)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 96, 288, 48
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6}*576e
32-fold quotients : {3,6}*36
96-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 7)( 6, 8)( 9,17)(10,18)(11,20)(12,19)(13,23)(14,24)(15,21)
(16,22);;
s1 := ( 1,11)( 2,12)( 3, 9)( 4,10)( 5,14)( 6,13)( 7,15)( 8,16)(17,19)(18,20)
(21,22);;
s2 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope