Questions?
See the FAQ
or other info.

# Polytope of Type {35,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,6,2}*1680
if this polytope has a name.
Group : SmallGroup(1680,931)
Rank : 4
Schlafli Type : {35,6,2}
Number of vertices, edges, etc : 70, 210, 12, 2
Order of s0s1s2s3 : 70
Order of s0s1s2s3s2s1 : 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) :
7-fold quotients : {5,6,2}*240b
14-fold quotients : {5,3,2}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 8, 9)(10,11);;
s2 := ( 9,12)(10,11);;
s3 := (13,14);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1,
s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope