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# Polytope of Type {12,6,2}

Atlas Canonical Name : {12,6,2}*864d
if this polytope has a name.
Group : SmallGroup(864,4000)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 36, 108, 18, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,6,2,2} of size 1728
Vertex Figure Of :
{2,12,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {12,6,2}*288d
4-fold quotients : {6,6,2}*216
9-fold quotients : {4,6,2}*96b
18-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,6,2}*1728b
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,27)(14,28)(15,25)(16,26)
(17,35)(18,36)(19,33)(20,34)(21,31)(22,32)(23,29)(24,30);;
s1 := ( 1,13)( 2,15)( 3,14)( 4,16)( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)
(11,22)(12,24)(26,27)(30,31)(34,35);;
s2 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,21)(14,24)(15,23)(16,22)(18,20)
(25,29)(26,32)(27,31)(28,30)(34,36);;
s3 := (37,38);;
poly := Group([s0,s1,s2,s3]);;

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

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

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

```

to this polytope