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# Polytope of Type {4,6}

Atlas Canonical Name : {4,6}*240a
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 20, 60, 30
Order of s0s1s2 : 10
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Facet Of :
{4,6,2} of size 480
{4,6,4} of size 960
{4,6,3} of size 1440
{4,6,4} of size 1440
{4,6,4} of size 1440
{4,6,6} of size 1440
{4,6,8} of size 1920
Vertex Figure Of :
{2,4,6} of size 480
{3,4,6} of size 720
{4,4,6} of size 960
{6,4,6} of size 1440
{6,4,6} of size 1440
{8,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6}*480
4-fold covers : {8,6}*960a, {4,6}*960, {4,12}*960a, {8,6}*960b, {4,12}*960b
6-fold covers : {4,6}*1440b, {12,6}*1440c, {12,6}*1440d
8-fold covers : {4,12}*1920a, {4,24}*1920a, {8,6}*1920a, {4,24}*1920b, {8,12}*1920a, {8,12}*1920b, {4,24}*1920c, {4,24}*1920d, {8,12}*1920c, {8,6}*1920b, {8,12}*1920d, {4,12}*1920b, {4,6}*1920
Permutation Representation (GAP) :
```s0 := (4,5);;
s1 := (2,4)(3,5);;
s2 := (1,2)(6,7);;
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*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope