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# Polytope of Type {7,16}

Atlas Canonical Name : {7,16}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {7,16}
Number of vertices, edges, etc : 42, 336, 96
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {7,8}*672b
4-fold quotients : {7,8}*336b
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 := ( 2, 4)( 3,21)( 6,30)( 7,13)( 8,20)( 9,24)(10,28)(11,19)(12,26)(15,29)
(16,32)(17,22)(23,31)(25,27);;
s2 := ( 1,11)( 2, 6)( 3, 4)( 5,25)( 7,30)( 8,28)( 9,27)(10,26)(12,16)(13,24)
(14,29)(15,21)(17,20)(18,32)(19,31)(22,23);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*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)!( 2, 4)( 3,21)( 6,30)( 7,13)( 8,20)( 9,24)(10,28)(11,19)(12,26)
(15,29)(16,32)(17,22)(23,31)(25,27);
s2 := Sym(32)!( 1,11)( 2, 6)( 3, 4)( 5,25)( 7,30)( 8,28)( 9,27)(10,26)(12,16)
(13,24)(14,29)(15,21)(17,20)(18,32)(19,31)(22,23);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope