Questions?
See the FAQ
or other info.

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

Atlas Canonical Name : {6,15,2,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 6
Schlafli Type : {6,15,2,2,2}
Number of vertices, edges, etc : 8, 60, 20, 2, 2, 2
Order of s0s1s2s3s4s5 : 20
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) :
5-fold quotients : {6,3,2,2,2}*384
10-fold quotients : {3,3,2,2,2}*192
12-fold quotients : {2,5,2,2,2}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20);;
s1 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);;
s2 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14);;
s3 := (21,22);;
s4 := (23,24);;
s5 := (25,26);;
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*s2*s0*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, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, 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*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(26)!( 3, 4)( 7, 8)(11,12)(15,16)(19,20);
s1 := Sym(26)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16);
s2 := Sym(26)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14);
s3 := Sym(26)!(21,22);
s4 := Sym(26)!(23,24);
s5 := Sym(26)!(25,26);
poly := sub<Sym(26)|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*s2*s0*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, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, 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*s2*s0*s1*s2*s1*s2 >;

```

to this polytope