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# Polytope of Type {2,6,15}

Atlas Canonical Name : {2,6,15}*1080
if this polytope has a name.
Group : SmallGroup(1080,337)
Rank : 4
Schlafli Type : {2,6,15}
Number of vertices, edges, etc : 2, 18, 135, 45
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 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 : {2,6,15}*360
5-fold quotients : {2,6,3}*216
9-fold quotients : {2,2,15}*120
15-fold quotients : {2,6,3}*72
27-fold quotients : {2,2,5}*40
45-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47);;
s2 := ( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)
(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)
(32,37);;
s3 := ( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)(12,27)
(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)
(41,47);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2,
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(47)!(1,2);
s1 := Sym(47)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);
s2 := Sym(47)!( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)
(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)
(32,37);
s3 := Sym(47)!( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)
(12,27)(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)
(41,47);
poly := sub<Sym(47)|s0,s1,s2,s3>;

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