Questions?
See the FAQ
or other info.

# Polytope of Type {2,5,2,6,6}

Atlas Canonical Name : {2,5,2,6,6}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 6
Schlafli Type : {2,5,2,6,6}
Number of vertices, edges, etc : 2, 5, 5, 6, 18, 6
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) :
2-fold quotients : {2,5,2,6,3}*720
3-fold quotients : {2,5,2,2,6}*480
6-fold quotients : {2,5,2,2,3}*240
9-fold quotients : {2,5,2,2,2}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
s3 := (12,13)(16,17)(18,19)(20,21)(22,23)(24,25);;
s4 := ( 8,12)( 9,16)(10,20)(11,18)(14,24)(15,22)(19,21)(23,25);;
s5 := ( 8,14)( 9,10)(11,15)(12,23)(13,22)(16,19)(17,18)(20,25)(21,24);;
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, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

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

```

to this polytope