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# Polytope of Type {2,2,2,6,9,2}

Atlas Canonical Name : {2,2,2,6,9,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46164)
Rank : 7
Schlafli Type : {2,2,2,6,9,2}
Number of vertices, edges, etc : 2, 2, 2, 6, 27, 9, 2
Order of s0s1s2s3s4s5s6 : 18
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 : {2,2,2,2,9,2}*576, {2,2,2,6,3,2}*576
9-fold quotients : {2,2,2,2,3,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(30,31)(32,33);;
s4 := ( 7,10)( 8,16)( 9,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)(24,32)
(26,29)(27,30)(31,33);;
s5 := ( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)
(28,31)(29,30)(32,33);;
s6 := (34,35);;
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, 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*s6*s0*s6, s1*s6*s1*s6,
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6,
s5*s6*s5*s6, 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*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(35)!(1,2);
s1 := Sym(35)!(3,4);
s2 := Sym(35)!(5,6);
s3 := Sym(35)!(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(30,31)(32,33);
s4 := Sym(35)!( 7,10)( 8,16)( 9,13)(12,22)(14,17)(15,19)(18,28)(20,23)(21,25)
(24,32)(26,29)(27,30)(31,33);
s5 := Sym(35)!( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(21,24)(22,26)
(23,25)(28,31)(29,30)(32,33);
s6 := Sym(35)!(34,35);
poly := sub<Sym(35)|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, 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*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6,
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6,
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*s4*s5*s4*s5*s4*s5 >;

```

to this polytope