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# Polytope of Type {16,3}

Atlas Canonical Name : {16,3}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {16,3}
Number of vertices, edges, etc : 224, 336, 42
Order of s0s1s2 : 16
Order of s0s1s2s1 : 16
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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 : {8,3}*672a
4-fold quotients : {8,3}*336a
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)
(16,24)(17,21)(23,25)(26,29);;
s1 := ( 1, 3)( 2,14)( 4,17)( 5, 7)( 6,31)( 8,11)( 9,15)(10,23)(12,30)(13,28)
(16,29)(18,24)(19,25)(20,32)(21,27)(22,26);;
s2 := ( 1,11)( 2, 6)( 3,23)( 4,17)( 5,15)( 7,30)( 8,10)( 9,12)(13,28)(14,27)
(16,29)(18,32)(19,25)(20,22)(21,31)(24,26);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(32)!( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)
(15,20)(16,24)(17,21)(23,25)(26,29);
s1 := Sym(32)!( 1, 3)( 2,14)( 4,17)( 5, 7)( 6,31)( 8,11)( 9,15)(10,23)(12,30)
(13,28)(16,29)(18,24)(19,25)(20,32)(21,27)(22,26);
s2 := Sym(32)!( 1,11)( 2, 6)( 3,23)( 4,17)( 5,15)( 7,30)( 8,10)( 9,12)(13,28)
(14,27)(16,29)(18,32)(19,25)(20,22)(21,31)(24,26);
poly := sub<Sym(32)|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, s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope