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# Polytope of Type {4,4,2}

Atlas Canonical Name : {4,4,2}*576
if this polytope has a name.
Group : SmallGroup(576,8418)
Rank : 4
Schlafli Type : {4,4,2}
Number of vertices, edges, etc : 36, 72, 36, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,4,2,2} of size 1152
{4,4,2,3} of size 1728
Vertex Figure Of :
{2,4,4,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,2}*288
4-fold quotients : {4,4,2}*144
9-fold quotients : {4,4,2}*64
18-fold quotients : {2,4,2}*32, {4,2,2}*32
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,4}*1152b, {4,8,2}*1152a, {8,4,2}*1152a, {4,8,2}*1152b, {8,4,2}*1152b, {4,4,2}*1152
3-fold covers : {4,12,2}*1728a, {12,4,2}*1728a, {4,12,2}*1728d, {12,4,2}*1728c, {4,4,6}*1728b
Permutation Representation (GAP) :
```s0 := ( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);;
s2 := ( 1, 2)( 4, 5)( 7,10)( 8,11)( 9,12);;
s3 := (13,14);;
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*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(14)!( 8, 9)(11,12);
s1 := Sym(14)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);
s2 := Sym(14)!( 1, 2)( 4, 5)( 7,10)( 8,11)( 9,12);
s3 := Sym(14)!(13,14);
poly := sub<Sym(14)|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*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

```

to this polytope