# Polytope of Type {5,10}

Atlas Canonical Name : {5,10}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 3
Schlafli Type : {5,10}
Number of vertices, edges, etc : 12, 60, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{5,10,2} of size 480
{5,10,4} of size 960
{5,10,6} of size 1440
{5,10,8} of size 1920
Vertex Figure Of :
{2,5,10} of size 480
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b
4-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,20}*480, {10,10}*480
3-fold covers : {15,10}*720
4-fold covers : {10,20}*960a, {20,10}*960a, {10,20}*960b, {20,10}*960b, {10,10}*960
5-fold covers : {5,10}*1200a, {5,10}*1200b
6-fold covers : {15,20}*1440a, {10,30}*1440, {30,10}*1440
7-fold covers : {35,10}*1680
8-fold covers : {20,20}*1920a, {10,40}*1920a, {40,10}*1920a, {10,20}*1920, {20,10}*1920, {20,20}*1920b, {20,20}*1920c, {20,20}*1920d, {10,40}*1920b, {40,10}*1920b
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(6,7)(8,9);;
s2 := (2,4)(3,5)(6,8)(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*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope