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# Polytope of Type {3,5,4}

Atlas Canonical Name : {3,5,4}*960
if this polytope has a name.
Group : SmallGroup(960,11358)
Rank : 4
Schlafli Type : {3,5,4}
Number of vertices, edges, etc : 6, 60, 80, 16
Order of s0s1s2s3 : 5
Order of s0s1s2s3s2s1 : 4
Special Properties :
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,5,4,2} of size 1920
Vertex Figure Of :
{2,3,5,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,5,4}*1920c, {3,5,4}*1920d, {3,10,4}*1920a, {3,10,4}*1920b, {3,10,4}*1920c, {3,10,4}*1920d, {6,5,4}*1920b, {6,5,4}*1920c
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,9)(7,8);;
s1 := ( 1, 2)( 4, 5)( 7, 8)( 9,10);;
s2 := (2,4)(3,5)(6,7)(8,9);;
s3 := (4,8)(5,7);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2,
s1*s0*s1*s2*s3*s2*s1*s0*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope