Questions?
See the FAQ
or other info.

# Polytope of Type {3,6,12,2}

Atlas Canonical Name : {3,6,12,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240594)
Rank : 5
Schlafli Type : {3,6,12,2}
Number of vertices, edges, etc : 5, 20, 80, 20, 2
Order of s0s1s2s3s4 : 20
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) :
2-fold quotients : {3,6,6,2}*960
4-fold quotients : {3,3,6,2}*480, {3,6,3,2}*480
8-fold quotients : {3,3,3,2}*240
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (7,9);;
s1 := (8,9);;
s2 := (2,3)(6,8);;
s3 := (1,2)(3,4)(5,6);;
s4 := (10,11);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(7,9);
s1 := Sym(11)!(8,9);
s2 := Sym(11)!(2,3)(6,8);
s3 := Sym(11)!(1,2)(3,4)(5,6);
s4 := Sym(11)!(10,11);
poly := sub<Sym(11)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

```

to this polytope