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# Polytope of Type {8,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,7}*1344
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {8,7}
Number of vertices, edges, etc : 96, 336, 84
Order of s0s1s2 : 16
Order of s0s1s2s1 : 12
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 : {4,7}*672
4-fold quotients : {4,7}*336
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)( 2,16)( 4,11)( 5,25)( 6,12)( 7,19)( 8,17)( 9,23)(10,15)(13,32)
(14,29)(18,24)(20,28)(21,26)(22,27)(30,31);;
s2 := ( 1,32)( 2, 6)( 3,27)( 4,14)( 5,13)( 7,30)( 8,19)( 9,23)(10,31)(11,18)
(12,22)(15,24)(16,20)(17,29)(21,26)(25,28);;
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*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*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)( 2,16)( 4,11)( 5,25)( 6,12)( 7,19)( 8,17)( 9,23)(10,15)
(13,32)(14,29)(18,24)(20,28)(21,26)(22,27)(30,31);
s2 := Sym(32)!( 1,32)( 2, 6)( 3,27)( 4,14)( 5,13)( 7,30)( 8,19)( 9,23)(10,31)
(11,18)(12,22)(15,24)(16,20)(17,29)(21,26)(25,28);
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*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;

```
References : None.
to this polytope