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

Atlas Canonical Name : {2,2,6,3,6,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,47915)
Rank : 7
Schlafli Type : {2,2,6,3,6,2}
Number of vertices, edges, etc : 2, 2, 6, 9, 9, 6, 2
Order of s0s1s2s3s4s5s6 : 6
Order of s0s1s2s3s4s5s6s5s4s3s2s1 : 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 : {2,2,2,3,6,2}*576, {2,2,6,3,2,2}*576
9-fold quotients : {2,2,2,3,2,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);;
s3 := ( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)(24,25)
(26,29)(27,31)(28,30);;
s4 := ( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)(19,25)
(20,30)(21,29)(22,31);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);;
s6 := (32,33);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, s0*s1*s0*s1, 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*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6,
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6,
s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(33)!(1,2);
s1 := Sym(33)!(3,4);
s2 := Sym(33)!(14,23)(15,24)(16,25)(17,26)(18,27)(19,28)(20,29)(21,30)(22,31);
s3 := Sym(33)!( 5,14)( 6,16)( 7,15)( 8,20)( 9,22)(10,21)(11,17)(12,19)(13,18)
(24,25)(26,29)(27,31)(28,30);
s4 := Sym(33)!( 5, 9)( 6, 8)( 7,10)(11,12)(14,27)(15,26)(16,28)(17,24)(18,23)
(19,25)(20,30)(21,29)(22,31);
s5 := Sym(33)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31);
s6 := Sym(33)!(32,33);
poly := sub<Sym(33)|s0,s1,s2,s3,s4,s5,s6>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s6*s6, s0*s1*s0*s1,
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*s6*s0*s6,
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6,
s4*s6*s4*s6, s5*s6*s5*s6, s3*s4*s3*s4*s3*s4,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4 >;

```

to this polytope