Questions?
See the FAQ
or other info.

# Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*192a
if this polytope has a name.
Group : SmallGroup(192,955)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 16, 48, 16
Order of s0s1s2 : 4
Order of s0s1s2s1 : 3
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,6,2} of size 384
Vertex Figure Of :
{2,6,6} of size 384
Quotients (Maximal Quotients in Boldface) :
8-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,6}*384a, {6,6}*384b, {6,6}*384c
4-fold covers : {6,6}*768a, {6,12}*768a, {6,12}*768b, {12,6}*768a, {12,6}*768b, {6,12}*768d, {12,6}*768d, {6,6}*768b, {6,12}*768f, {12,6}*768f, {6,6}*768e, {6,12}*768i, {12,6}*768i, {6,6}*768f, {6,12}*768j, {12,6}*768j
6-fold covers : {6,6}*1152c, {6,6}*1152d
10-fold covers : {6,30}*1920b, {30,6}*1920b
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);;
s2 := ( 1,11)( 2,12)( 3, 9)( 4,10);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!( 1, 9)( 2,10)( 3,11)( 4,12);
s1 := Sym(12)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11);
s2 := Sym(12)!( 1,11)( 2,12)( 3, 9)( 4,10);
poly := sub<Sym(12)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

```
References : None.
to this polytope