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# Polytope of Type {8,15}

Atlas Canonical Name : {8,15}*1440
if this polytope has a name.
Group : SmallGroup(1440,4612)
Rank : 3
Schlafli Type : {8,15}
Number of vertices, edges, etc : 48, 360, 90
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 : {4,15}*720
3-fold quotients : {8,5}*480
6-fold quotients : {4,5}*240
12-fold quotients : {4,5}*120
120-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)(12,28)
(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);;
s1 := ( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)(22,37)
(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);;
s2 := ( 1,12)( 2,11)( 3, 9)( 4,10)( 5,23)( 6,24)( 7,22)( 8,21)(13,28)(14,25)
(15,27)(16,26)(17,31)(18,32)(19,30)(20,29)(33,36)(34,35)(41,42);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(43)!( 1,13)( 2,14)( 3,16)( 4,15)( 5, 7)( 6, 8)( 9,26)(10,27)(11,25)
(12,28)(17,32)(18,31)(19,30)(20,29)(21,24)(22,23)(33,34)(35,36)(38,40);
s1 := Sym(43)!( 5,10)( 6, 9)( 7,11)( 8,12)(13,18)(14,17)(15,20)(16,19)(21,39)
(22,37)(23,40)(24,38)(25,36)(26,35)(27,34)(28,33)(29,30)(31,32)(42,43);
s2 := Sym(43)!( 1,12)( 2,11)( 3, 9)( 4,10)( 5,23)( 6,24)( 7,22)( 8,21)(13,28)
(14,25)(15,27)(16,26)(17,31)(18,32)(19,30)(20,29)(33,36)(34,35)(41,42);
poly := sub<Sym(43)|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*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1 >;

```
References : None.
to this polytope