Questions?
See the FAQ
or other info.

# Polytope of Type {7,2,10,4}

Atlas Canonical Name : {7,2,10,4}*1120
if this polytope has a name.
Group : SmallGroup(1120,998)
Rank : 5
Schlafli Type : {7,2,10,4}
Number of vertices, edges, etc : 7, 7, 10, 20, 4
Order of s0s1s2s3s4 : 140
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 : {7,2,10,2}*560
4-fold quotients : {7,2,5,2}*280
5-fold quotients : {7,2,2,4}*224
10-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (10,11)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := ( 8,10)( 9,18)(11,15)(12,13)(14,24)(17,22)(19,20)(21,25)(23,26);;
s4 := ( 8, 9)(10,13)(11,14)(12,17)(15,20)(16,21)(18,22)(19,23)(24,26)(25,27);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(27)!(2,3)(4,5)(6,7);
s1 := Sym(27)!(1,2)(3,4)(5,6);
s2 := Sym(27)!(10,11)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27);
s3 := Sym(27)!( 8,10)( 9,18)(11,15)(12,13)(14,24)(17,22)(19,20)(21,25)(23,26);
s4 := Sym(27)!( 8, 9)(10,13)(11,14)(12,17)(15,20)(16,21)(18,22)(19,23)(24,26)
(25,27);
poly := sub<Sym(27)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope