# Polytope of Type {2,5,10,2,2}

Atlas Canonical Name : {2,5,10,2,2}*960a
if this polytope has a name.
Group : SmallGroup(960,11356)
Rank : 6
Schlafli Type : {2,5,10,2,2}
Number of vertices, edges, etc : 2, 6, 30, 12, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,5,10,2,2,2} of size 1920
Vertex Figure Of :
{2,2,5,10,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,5,5,2,2}*480
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,5,10,2,4}*1920a, {2,5,10,2,2}*1920, {2,10,10,2,2}*1920c, {2,10,10,2,2}*1920d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4,11)( 6,14)( 7, 9)( 8,10);;
s2 := ( 5, 7)( 6,13)( 8,14)( 9,11);;
s3 := ( 3, 5)( 4,10)( 6,14)( 7, 9)( 8,11)(12,13);;
s4 := (15,16);;
s5 := (17,18);;
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, 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, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope