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# Polytope of Type {6,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,4}*288
if this polytope has a name.
Group : SmallGroup(288,889)
Rank : 4
Schlafli Type : {6,4,4}
Number of vertices, edges, etc : 9, 18, 12, 4
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,4,2} of size 576
{6,4,4,4} of size 1152
{6,4,4,6} of size 1728
{6,4,4,3} of size 1728
Vertex Figure Of :
{2,6,4,4} of size 576
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4,2}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,4,8}*576, {6,4,4}*576
3-fold covers : {6,4,4}*864a, {6,12,4}*864a, {6,12,4}*864b, {6,4,12}*864, {6,12,4}*864c
4-fold covers : {6,4,16}*1152, {12,4,4}*1152, {6,4,8}*1152a, {6,8,4}*1152a, {6,4,8}*1152b, {6,8,4}*1152b, {6,4,4}*1152a
5-fold covers : {6,4,20}*1440, {6,20,4}*1440
6-fold covers : {6,4,8}*1728, {6,12,8}*1728a, {6,12,8}*1728b, {6,4,4}*1728a, {6,12,4}*1728h, {6,12,4}*1728i, {6,4,24}*1728, {6,12,8}*1728c, {6,4,12}*1728a, {6,4,4}*1728c, {6,12,4}*1728o, {6,12,4}*1728q
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12);;
s1 := ( 7, 8)(10,11);;
s2 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);;
s3 := ( 7,10)( 8,11)( 9,12);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!( 2, 3)( 5, 6)( 8, 9)(11,12);
s1 := Sym(12)!( 7, 8)(10,11);
s2 := Sym(12)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);
s3 := Sym(12)!( 7,10)( 8,11)( 9,12);
poly := sub<Sym(12)|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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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*s0*s1*s2*s0*s1*s0*s1 >;

```
References : None.
to this polytope