# Polytope of Type {6,12,2}

Atlas Canonical Name : {6,12,2}*864h
if this polytope has a name.
Group : SmallGroup(864,4686)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 18, 108, 36, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,12,2,2} of size 1728
Vertex Figure Of :
{2,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {6,4,2}*288
6-fold quotients : {6,4,2}*144
27-fold quotients : {2,4,2}*32
54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12,2}*1728j, {6,24,2}*1728g, {6,12,4}*1728o
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);;
s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(14,15)(17,18);;
s3 := (19,20);;
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,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope