# Polytope of Type {4,6,5}

Atlas Canonical Name : {4,6,5}*480b
if this polytope has a name.
Group : SmallGroup(480,956)
Rank : 4
Schlafli Type : {4,6,5}
Number of vertices, edges, etc : 4, 24, 30, 10
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,5,2} of size 960
Vertex Figure Of :
{2,4,6,5} of size 960
{4,4,6,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,5}*240b
4-fold quotients : {2,3,5}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,6,5}*960b, {4,6,5}*960b, {4,6,10}*960c, {4,6,10}*960d
3-fold covers : {12,6,5}*1440b
4-fold covers : {16,6,5}*1920b, {4,12,10}*1920f, {4,12,10}*1920g, {8,6,5}*1920b, {8,6,10}*1920e, {8,6,10}*1920f, {4,6,10}*1920d, {4,12,5}*1920
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2)(3,4)(6,7)(8,9);;
s2 := (5,6)(8,9);;
s3 := (6,8)(7,9);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope