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

Atlas Canonical Name : {6,6,2,5}*720b
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 5
Schlafli Type : {6,6,2,5}
Number of vertices, edges, etc : 6, 18, 6, 5, 5
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,6,2,5,2} of size 1440
Vertex Figure Of :
{2,6,6,2,5} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,3,2,5}*360
3-fold quotients : {2,6,2,5}*240
6-fold quotients : {2,3,2,5}*120
9-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,12,2,5}*1440b, {12,6,2,5}*1440c, {6,6,2,10}*1440b
Permutation Representation (GAP) :
```s0 := ( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s1 := ( 1, 5)( 2, 9)( 3,13)( 4,11)( 7,17)( 8,15)(12,14)(16,18);;
s2 := ( 1, 7)( 2, 3)( 4, 8)( 5,16)( 6,15)( 9,12)(10,11)(13,18)(14,17);;
s3 := (20,21)(22,23);;
s4 := (19,20)(21,22);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, 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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope