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# Polytope of Type {10,4}

Atlas Canonical Name : {10,4}*240a
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {10,4}
Number of vertices, edges, etc : 30, 60, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{10,4,2} of size 480
{10,4,4} of size 960
{10,4,6} of size 1440
{10,4,8} of size 1920
Vertex Figure Of :
{2,10,4} of size 480
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,4}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,4}*480a, {10,4}*480b, {10,4}*480c
3-fold covers : {10,12}*720
4-fold covers : {10,8}*960a, {10,8}*960b, {20,4}*960a, {20,4}*960b, {10,8}*960c, {10,8}*960d, {20,4}*960c, {20,4}*960d, {10,4}*960
5-fold covers : {10,20}*1200
6-fold covers : {10,12}*1440b, {10,12}*1440d, {10,12}*1440g, {30,4}*1440
7-fold covers : {10,28}*1680
8-fold covers : {10,16}*1920a, {10,16}*1920b, {20,4}*1920a, {10,8}*1920a, {40,4}*1920a, {40,4}*1920b, {10,8}*1920b, {20,4}*1920b, {10,4}*1920, {20,8}*1920a, {20,8}*1920b, {20,8}*1920c, {20,8}*1920d, {40,4}*1920c, {40,4}*1920d
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4)(6,7);;
s2 := (2,3);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
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)!(2,3)(4,5);
s1 := Sym(7)!(1,2)(3,4)(6,7);
s2 := Sym(7)!(2,3);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope