Polytope of Type {4,10}

Atlas Canonical Name : {4,10}*480c
if this polytope has a name.
Group : SmallGroup(480,1186)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 24, 120, 60
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 :
{4,10,2} of size 960
{4,10,4} of size 1920
Vertex Figure Of :
{2,4,10} of size 960
{4,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
4-fold quotients : {4,5}*120
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,10}*960c, {8,10}*960d, {4,20}*960c, {4,20}*960d, {4,10}*960
3-fold covers : {4,30}*1440, {12,10}*1440g
4-fold covers : {4,20}*1920a, {8,10}*1920a, {4,40}*1920a, {4,40}*1920b, {8,10}*1920b, {4,20}*1920b, {4,10}*1920, {8,20}*1920a, {8,20}*1920b, {8,20}*1920c, {8,20}*1920d, {4,40}*1920c, {4,40}*1920d
Permutation Representation (GAP) :
```s0 := (3,5);;
s1 := (2,3)(4,5)(6,7)(8,9);;
s2 := (1,2)(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,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope