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# Polytope of Type {4,10}

Atlas Canonical Name : {4,10}*480a
if this polytope has a name.
Group : SmallGroup(480,951)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 24, 120, 60
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Facet Of :
{4,10,2} of size 960
Vertex Figure Of :
{2,4,10} of size 960
{4,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,10}*240b
4-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,10}*960a, {8,10}*960b, {4,10}*960
3-fold covers : {12,10}*1440a
4-fold covers : {16,10}*1920a, {16,10}*1920b, {4,20}*1920a, {8,10}*1920a, {8,10}*1920b, {4,20}*1920b, {4,10}*1920
Permutation Representation (GAP) :
```s0 := (3,4)(7,9);;
s1 := (1,3)(2,4)(6,7)(8,9);;
s2 := (5,6)(7,9);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope