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# Polytope of Type {10,4}

Atlas Canonical Name : {10,4}*960
if this polytope has a name.
Group : SmallGroup(960,10882)
Rank : 3
Schlafli Type : {10,4}
Number of vertices, edges, etc : 120, 240, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{10,4,2} of size 1920
Vertex Figure Of :
{2,10,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,4}*480a, {10,4}*480b, {10,4}*480c
4-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
8-fold quotients : {5,4}*120
60-fold quotients : {2,4}*16
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,4}*1920a, {10,8}*1920a, {10,8}*1920b, {20,4}*1920b, {10,4}*1920
Permutation Representation (GAP) :
```s0 := ( 6, 7)( 8, 9)(10,11);;
s1 := (1,3)(2,4)(5,6)(7,8);;
s2 := (3,4)(6,7);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;

```
References : None.
to this polytope