# Polytope of Type {5,10,6}

Atlas Canonical Name : {5,10,6}*720
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 4
Schlafli Type : {5,10,6}
Number of vertices, edges, etc : 6, 30, 36, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,10,6,2} of size 1440
Vertex Figure Of :
{2,5,10,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {5,10,2}*240b
6-fold quotients : {5,5,2}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,10,12}*1440, {5,10,6}*1440, {10,10,6}*1440a, {10,10,6}*1440b
Permutation Representation (GAP) :
```s0 := ( 7, 8)( 9,10);;
s1 := (6,7)(8,9);;
s2 := ( 4, 5)( 7, 9)( 8,10);;
s3 := (1,2)(3,4);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(10)!( 7, 8)( 9,10);
s1 := Sym(10)!(6,7)(8,9);
s2 := Sym(10)!( 4, 5)( 7, 9)( 8,10);
s3 := Sym(10)!(1,2)(3,4);
poly := sub<Sym(10)|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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0 >;

```
References : None.
to this polytope