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# Polytope of Type {4,6}

Atlas Canonical Name : {4,6}*192a
if this polytope has a name.
Group : SmallGroup(192,955)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 16, 48, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
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 384
{4,6,3} of size 576
{4,6,4} of size 768
{4,6,4} of size 768
{4,6,6} of size 1152
{4,6,6} of size 1152
{4,6,4} of size 1152
{4,6,6} of size 1152
{4,6,9} of size 1728
{4,6,3} of size 1728
{4,6,10} of size 1920
{4,6,4} of size 1920
Vertex Figure Of :
{2,4,6} of size 384
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {4,6}*48c
8-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12}*384b, {4,12}*384c, {8,6}*384b, {8,6}*384c, {4,6}*384a
3-fold covers : {4,18}*576a
4-fold covers : {4,24}*768e, {4,24}*768f, {8,12}*768e, {8,12}*768f, {8,12}*768g, {8,12}*768h, {4,24}*768g, {4,24}*768h, {8,6}*768a, {8,6}*768b, {8,6}*768c, {8,12}*768i, {8,12}*768j, {8,6}*768e, {8,6}*768g, {4,12}*768b, {4,6}*768a, {4,12}*768c, {8,6}*768m, {8,6}*768n, {4,6}*768b, {4,6}*768c, {4,12}*768g, {4,12}*768h
5-fold covers : {4,30}*960a
6-fold covers : {4,36}*1152b, {4,36}*1152c, {8,18}*1152b, {8,18}*1152c, {4,18}*1152a, {12,6}*1152b, {12,6}*1152c
7-fold covers : {4,42}*1344a
9-fold covers : {4,54}*1728a
10-fold covers : {4,60}*1920b, {4,60}*1920c, {8,30}*1920b, {8,30}*1920c, {20,6}*1920a, {4,30}*1920a
Permutation Representation (GAP) :
```s0 := ( 5, 7)( 6, 8)( 9,11)(10,12);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s2 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
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,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope