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# Polytope of Type {2,4,14,2,3}

Atlas Canonical Name : {2,4,14,2,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 6
Schlafli Type : {2,4,14,2,3}
Number of vertices, edges, etc : 2, 4, 28, 14, 3, 3
Order of s0s1s2s3s4s5 : 84
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,14,2,3}*672
4-fold quotients : {2,2,7,2,3}*336
7-fold quotients : {2,4,2,2,3}*192
14-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 7)( 8,13)( 9,14)(15,21)(16,22)(23,27)(24,28);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 7,12)(10,16)(11,15)(13,20)(14,19)(17,24)(18,23)
(21,26)(22,25)(27,30)(28,29);;
s3 := ( 3, 5)( 4, 8)( 6,10)( 7,13)( 9,15)(11,17)(12,19)(14,21)(16,23)(20,25)
(22,27)(26,29);;
s4 := (32,33);;
s5 := (31,32);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, 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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*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(33)!(1,2);
s1 := Sym(33)!( 4, 7)( 8,13)( 9,14)(15,21)(16,22)(23,27)(24,28);
s2 := Sym(33)!( 3, 4)( 5, 9)( 6, 8)( 7,12)(10,16)(11,15)(13,20)(14,19)(17,24)
(18,23)(21,26)(22,25)(27,30)(28,29);
s3 := Sym(33)!( 3, 5)( 4, 8)( 6,10)( 7,13)( 9,15)(11,17)(12,19)(14,21)(16,23)
(20,25)(22,27)(26,29);
s4 := Sym(33)!(32,33);
s5 := Sym(33)!(31,32);
poly := sub<Sym(33)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope