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# Polytope of Type {2,2,6,12}

Atlas Canonical Name : {2,2,6,12}*1728d
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {2,2,6,12}
Number of vertices, edges, etc : 2, 2, 18, 108, 36
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,2,6,12}*576d
4-fold quotients : {2,2,6,6}*432
9-fold quotients : {2,2,6,4}*192b
18-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,25)(22,27)(23,26)(24,28)
(30,31)(33,37)(34,39)(35,38)(36,40);;
s3 := ( 7, 8)(11,12)(15,16)(17,37)(18,38)(19,40)(20,39)(21,29)(22,30)(23,32)
(24,31)(25,33)(26,34)(27,36)(28,35);;
s4 := ( 5,20)( 6,19)( 7,18)( 8,17)( 9,28)(10,27)(11,26)(12,25)(13,24)(14,23)
(15,22)(16,21)(29,32)(30,31)(33,40)(34,39)(35,38)(36,37);;
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*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,25)(22,27)(23,26)
(24,28)(30,31)(33,37)(34,39)(35,38)(36,40);
s3 := Sym(40)!( 7, 8)(11,12)(15,16)(17,37)(18,38)(19,40)(20,39)(21,29)(22,30)
(23,32)(24,31)(25,33)(26,34)(27,36)(28,35);
s4 := Sym(40)!( 5,20)( 6,19)( 7,18)( 8,17)( 9,28)(10,27)(11,26)(12,25)(13,24)
(14,23)(15,22)(16,21)(29,32)(30,31)(33,40)(34,39)(35,38)(36,37);
poly := sub<Sym(40)|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*s4*s2*s3*s4*s2*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope