# Polytope of Type {3,2,2,6,6}

Atlas Canonical Name : {3,2,2,6,6}*864b
if this polytope has a name.
Group : SmallGroup(864,4704)
Rank : 6
Schlafli Type : {3,2,2,6,6}
Number of vertices, edges, etc : 3, 3, 2, 6, 18, 6
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,6,6,2} of size 1728
Vertex Figure Of :
{2,3,2,2,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,6,3}*432
3-fold quotients : {3,2,2,2,6}*288
6-fold quotients : {3,2,2,2,3}*144
9-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,2,6,12}*1728b, {3,2,2,12,6}*1728c, {3,2,4,6,6}*1728c, {6,2,2,6,6}*1728b
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (10,11)(14,15)(16,17)(18,19)(20,21)(22,23);;
s4 := ( 6,10)( 7,14)( 8,18)( 9,16)(12,22)(13,20)(17,19)(21,23);;
s5 := ( 6,12)( 7, 8)( 9,13)(10,21)(11,20)(14,17)(15,16)(18,23)(19,22);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(23)!(2,3);
s1 := Sym(23)!(1,2);
s2 := Sym(23)!(4,5);
s3 := Sym(23)!(10,11)(14,15)(16,17)(18,19)(20,21)(22,23);
s4 := Sym(23)!( 6,10)( 7,14)( 8,18)( 9,16)(12,22)(13,20)(17,19)(21,23);
s5 := Sym(23)!( 6,12)( 7, 8)( 9,13)(10,21)(11,20)(14,17)(15,16)(18,23)(19,22);
poly := sub<Sym(23)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

```

to this polytope