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# Polytope of Type {4,10,6}

Atlas Canonical Name : {4,10,6}*960c
if this polytope has a name.
Group : SmallGroup(960,10886)
Rank : 4
Schlafli Type : {4,10,6}
Number of vertices, edges, etc : 4, 40, 60, 12
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,10,6,2} of size 1920
Vertex Figure Of :
{2,4,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,10,3}*480, {2,10,6}*480e
4-fold quotients : {2,5,6}*240b, {2,10,3}*240a
8-fold quotients : {2,5,3}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,20,6}*1920d, {4,20,6}*1920e, {8,10,6}*1920c, {4,10,6}*1920c
Permutation Representation (GAP) :
```s0 := (4,6);;
s1 := ( 3, 4)( 5, 6)( 8, 9)(10,11);;
s2 := ( 1, 2)( 7, 8)( 9,10);;
s3 := ( 8,11)( 9,10);;
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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

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

```
References : None.
to this polytope