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# Polytope of Type {10,6,4}

Atlas Canonical Name : {10,6,4}*960c
if this polytope has a name.
Group : SmallGroup(960,10886)
Rank : 4
Schlafli Type : {10,6,4}
Number of vertices, edges, etc : 20, 60, 24, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,6,4,2} of size 1920
Vertex Figure Of :
{2,10,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,6,4}*480b, {10,6,2}*480c
4-fold quotients : {5,6,2}*240c, {10,3,2}*240b
8-fold quotients : {5,3,2}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,12,4}*1920f, {10,12,4}*1920g, {10,6,8}*1920e, {10,6,4}*1920d
Permutation Representation (GAP) :
```s0 := ( 8, 9)(10,11);;
s1 := ( 1, 2)( 7, 8)( 9,10);;
s2 := ( 4, 6)( 8,11)( 9,10);;
s3 := (3,4)(5,6);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!( 8, 9)(10,11);
s1 := Sym(11)!( 1, 2)( 7, 8)( 9,10);
s2 := Sym(11)!( 4, 6)( 8,11)( 9,10);
s3 := Sym(11)!(3,4)(5,6);
poly := sub<Sym(11)|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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 >;

```
References : None.
to this polytope