# Polytope of Type {24,10}

Atlas Canonical Name : {24,10}*960a
if this polytope has a name.
Group : SmallGroup(960,5713)
Rank : 3
Schlafli Type : {24,10}
Number of vertices, edges, etc : 48, 240, 20
Order of s0s1s2 : 8
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{24,10,2} of size 1920
Vertex Figure Of :
{2,24,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,10}*480a
4-fold quotients : {6,10}*240b
8-fold quotients : {6,5}*120a
Covers (Minimal Covers in Boldface) :
2-fold covers : {48,10}*1920a, {48,10}*1920b, {24,10}*1920c
Permutation Representation (GAP) :
```s0 := ( 2, 7)( 3, 5)( 6, 8)(11,12);;
s1 := ( 1, 2)( 3, 4)( 5, 8)( 6, 7)( 9,10)(12,13);;
s2 := (10,13)(11,12);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope