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# Polytope of Type {10,12,4}

Atlas Canonical Name : {10,12,4}*1920g
if this polytope has a name.
Group : SmallGroup(1920,240508)
Rank : 4
Schlafli Type : {10,12,4}
Number of vertices, edges, etc : 20, 120, 48, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,6,4}*960c, {10,12,2}*960d
4-fold quotients : {5,6,4}*480b, {10,6,2}*480c
8-fold quotients : {5,6,2}*240c, {10,3,2}*240b
16-fold quotients : {5,3,2}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 4)( 2, 7)( 3, 8)( 5, 6)(10,11)(12,13);;
s1 := ( 1, 6)( 2, 8)( 3, 7)( 4, 5)( 9,12)(10,13);;
s2 := ( 1, 8)( 2, 5)( 3, 4)( 6, 7)(10,13)(11,12);;
s3 := (1,6)(2,7)(3,8)(4,5);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(13)!( 1, 4)( 2, 7)( 3, 8)( 5, 6)(10,11)(12,13);
s1 := Sym(13)!( 1, 6)( 2, 8)( 3, 7)( 4, 5)( 9,12)(10,13);
s2 := Sym(13)!( 1, 8)( 2, 5)( 3, 4)( 6, 7)(10,13)(11,12);
s3 := Sym(13)!(1,6)(2,7)(3,8)(4,5);
poly := sub<Sym(13)|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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope