# Polytope of Type {4,2,6,6}

Atlas Canonical Name : {4,2,6,6}*576c
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 5
Schlafli Type : {4,2,6,6}
Number of vertices, edges, etc : 4, 4, 6, 18, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,6,6,2} of size 1152
{4,2,6,6,3} of size 1728
Vertex Figure Of :
{2,4,2,6,6} of size 1152
{3,4,2,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,3,6}*288, {2,2,6,6}*288c
3-fold quotients : {4,2,6,2}*192
4-fold quotients : {2,2,3,6}*144
6-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
9-fold quotients : {4,2,2,2}*64
12-fold quotients : {2,2,3,2}*48
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,6,6}*1152b, {4,2,6,12}*1152a, {4,2,12,6}*1152c, {8,2,6,6}*1152c
3-fold covers : {4,2,18,6}*1728b, {4,2,6,6}*1728c, {12,2,6,6}*1728c, {4,6,6,6}*1728e, {4,2,6,6}*1728d, {4,6,6,6}*1728h
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,22)(20,21);;
s3 := ( 5,19)( 6,15)( 7,13)( 8,21)( 9,11)(10,20)(12,17)(14,16)(18,22);;
s4 := ( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(22)!(2,3);
s1 := Sym(22)!(1,2)(3,4);
s2 := Sym(22)!( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,22)(20,21);
s3 := Sym(22)!( 5,19)( 6,15)( 7,13)( 8,21)( 9,11)(10,20)(12,17)(14,16)(18,22);
s4 := Sym(22)!( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22);
poly := sub<Sym(22)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >;

```

to this polytope