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# Polytope of Type {3,6}

Atlas Canonical Name : {3,6}*192
Also Known As : {3,6}(4,0), {3,6}8if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {3,6}
Number of vertices, edges, etc : 16, 48, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
Special Properties :
Toroidal
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,6,2} of size 384
{3,6,4} of size 768
{3,6,6} of size 1152
{3,6,10} of size 1920
Vertex Figure Of :
{2,3,6} of size 384
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {3,6}*48
8-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,12}*384, {6,6}*384e
3-fold covers : {3,6}*576
4-fold covers : {3,24}*768, {3,6}*768, {6,12}*768c, {12,6}*768e, {6,6}*768c, {6,12}*768g, {12,6}*768h
5-fold covers : {15,6}*960
6-fold covers : {3,12}*1152a, {6,6}*1152a, {6,6}*1152e
7-fold covers : {21,6}*1344
9-fold covers : {9,6}*1728, {3,6}*1728
10-fold covers : {15,12}*1920, {30,6}*1920a, {6,30}*1920c
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 5, 9)( 6,10)( 7,12)( 8,11);;
s2 := ( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*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(12)!( 1, 9)( 2,10)( 3,11)( 4,12);
s1 := Sym(12)!( 5, 9)( 6,10)( 7,12)( 8,11);
s2 := Sym(12)!( 1,11)( 2,12)( 3, 9)( 4,10)( 5, 6);
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, 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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

```
References : None.
to this polytope