Questions?
See the FAQ
or other info.

# Polytope of Type {6,6,6}

Atlas Canonical Name : {6,6,6}*960
if this polytope has a name.
Group : SmallGroup(960,11355)
Rank : 4
Schlafli Type : {6,6,6}
Number of vertices, edges, etc : 10, 40, 40, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 6
Special Properties :
Universal
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,6,6,2} of size 1920
Vertex Figure Of :
{2,6,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,6,6}*480, {6,3,6}*480, {6,6,3}*480
4-fold quotients : {3,3,6}*240, {3,6,3}*240, {6,3,3}*240
8-fold quotients : {3,3,3}*120
60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,6,12}*1920, {6,12,6}*1920a, {12,6,6}*1920, {6,12,6}*1920b
Permutation Representation (GAP) :
```s0 := ( 9,11);;
s1 := ( 3, 4)( 5, 6)(10,11);;
s2 := ( 3, 5)( 4, 6)( 8,10);;
s3 := (1,2)(7,8);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!( 9,11);
s1 := Sym(11)!( 3, 4)( 5, 6)(10,11);
s2 := Sym(11)!( 3, 5)( 4, 6)( 8,10);
s3 := Sym(11)!(1,2)(7,8);
poly := sub<Sym(11)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 >;

```
References : None.
to this polytope