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# Polytope of Type {2,2,4,12}

Atlas Canonical Name : {2,2,4,12}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47887)
Rank : 5
Schlafli Type : {2,2,4,12}
Number of vertices, edges, etc : 2, 2, 18, 108, 54
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,4,4}*576
6-fold quotients : {2,2,4,4}*288
18-fold quotients : {2,2,2,6}*96
36-fold quotients : {2,2,2,3}*48
54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8,11)( 9,12)(10,13);;
s3 := ( 5,14)( 6,16)( 7,15)( 8,17)( 9,19)(10,18)(11,20)(12,22)(13,21);;
s4 := ( 5, 6)( 8, 9)(11,12)(14,21)(15,20)(16,22)(17,18);;
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*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, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3*s4*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope