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# Polytope of Type {14,4,2,7}

Atlas Canonical Name : {14,4,2,7}*1568
if this polytope has a name.
Group : SmallGroup(1568,858)
Rank : 5
Schlafli Type : {14,4,2,7}
Number of vertices, edges, etc : 14, 28, 4, 7, 7
Order of s0s1s2s3s4 : 28
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 : {14,2,2,7}*784
4-fold quotients : {7,2,2,7}*392
7-fold quotients : {2,4,2,7}*224
14-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)
(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)
(19,23)(20,24)(25,27)(26,28);;
s3 := (30,31)(32,33)(34,35);;
s4 := (29,30)(31,32)(33,34);;
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, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(35)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s1 := Sym(35)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)
(18,23)(20,21)(22,26)(24,27);
s2 := Sym(35)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)
(16,22)(19,23)(20,24)(25,27)(26,28);
s3 := Sym(35)!(30,31)(32,33)(34,35);
s4 := Sym(35)!(29,30)(31,32)(33,34);
poly := sub<Sym(35)|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, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope