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

Atlas Canonical Name : {3,2,6,6,3}*1296b
if this polytope has a name.
Group : SmallGroup(1296,3538)
Rank : 6
Schlafli Type : {3,2,6,6,3}
Number of vertices, edges, etc : 3, 3, 6, 18, 9, 3
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,2,2,6,3}*432, {3,2,6,2,3}*432
6-fold quotients : {3,2,3,2,3}*216
9-fold quotients : {3,2,2,2,3}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30);;
s3 := ( 4,13)( 5,14)( 6,15)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)(25,28)
(26,29)(27,30);;
s4 := ( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)(23,27)
(24,26)(29,30);;
s5 := ( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,20)(17,19)(18,21)(22,23)(25,29)
(26,28)(27,30);;
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, 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,
s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(30)!(2,3);
s1 := Sym(30)!(1,2);
s2 := Sym(30)!(13,22)(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30);
s3 := Sym(30)!( 4,13)( 5,14)( 6,15)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)
(25,28)(26,29)(27,30);
s4 := Sym(30)!( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)
(23,27)(24,26)(29,30);
s5 := Sym(30)!( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,20)(17,19)(18,21)(22,23)
(25,29)(26,28)(27,30);
poly := sub<Sym(30)|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, 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, s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope