# Polytope of Type {6,6}

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

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

```
References : None.
to this polytope