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# Polytope of Type {16,4,5}

Atlas Canonical Name : {16,4,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240469)
Rank : 4
Schlafli Type : {16,4,5}
Number of vertices, edges, etc : 16, 96, 30, 15
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
2-fold quotients : {8,4,5}*960
4-fold quotients : {4,4,5}*480
8-fold quotients : {2,4,5}*240
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)(23,31)
(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);;
s1 := ( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)
(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);;
s2 := (2,4)(3,5);;
s3 := (1,2)(4,5);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(37)!( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)(22,30)
(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);
s1 := Sym(37)!( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)
(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);
s2 := Sym(37)!(2,4)(3,5);
s3 := Sym(37)!(1,2)(4,5);
poly := sub<Sym(37)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*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*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope