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# Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240594)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 24, 240, 120
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 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 : {2,4,10}*960c
4-fold quotients : {2,4,5}*480, {2,4,10}*480a, {2,4,10}*480b
8-fold quotients : {2,4,5}*240
60-fold quotients : {2,2,4}*32
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 9,11);;
s2 := ( 4, 5)( 8, 9)(10,11);;
s3 := ( 3, 4)( 5, 6)( 7, 8)( 9,11);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2,
s3*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1 ];;
poly := F / rels;;

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

```

to this polytope