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# Polytope of Type {2,2,15,6,2}

Atlas Canonical Name : {2,2,15,6,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,5949)
Rank : 6
Schlafli Type : {2,2,15,6,2}
Number of vertices, edges, etc : 2, 2, 15, 45, 6, 2
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,15,2,2}*480
5-fold quotients : {2,2,3,6,2}*288
9-fold quotients : {2,2,5,2,2}*160
15-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)
(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)
(34,41);;
s3 := ( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)(14,22)
(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)
(47,49);;
s4 := (20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)
(30,45)(31,46)(32,47)(33,48)(34,49);;
s5 := (50,51);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(51)!(1,2);
s1 := Sym(51)!(3,4);
s2 := Sym(51)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)
(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)
(33,42)(34,41);
s3 := Sym(51)!( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)
(14,22)(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)
(45,46)(47,49);
s4 := Sym(51)!(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)
(29,44)(30,45)(31,46)(32,47)(33,48)(34,49);
s5 := Sym(51)!(50,51);
poly := sub<Sym(51)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope