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# Polytope of Type {6,15,2}

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

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

```

to this polytope