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

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

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

```

to this polytope