Questions?
See the FAQ
or other info.

# Polytope of Type {2,12,6}

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

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

```

to this polytope