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# Polytope of Type {4,10}

Atlas Canonical Name : {4,10}*240b
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {4,10}
Number of vertices, edges, etc : 12, 60, 30
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{4,10,2} of size 480
Vertex Figure Of :
{2,4,10} of size 480
{4,4,10} of size 960
{6,4,10} of size 1440
{8,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,10}*480a, {4,10}*480b, {4,10}*480c
3-fold covers : {12,10}*720
4-fold covers : {8,10}*960a, {8,10}*960b, {4,20}*960a, {4,20}*960b, {8,10}*960c, {8,10}*960d, {4,20}*960c, {4,20}*960d, {4,10}*960
5-fold covers : {20,10}*1200
6-fold covers : {12,10}*1440a, {12,10}*1440b, {4,30}*1440, {12,10}*1440g
7-fold covers : {28,10}*1680
8-fold covers : {16,10}*1920a, {16,10}*1920b, {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 := (4,5);;
s1 := (2,4)(3,5)(6,7);;
s2 := (1,2)(4,5);;
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,
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope