# Polytope of Type {20,2,5}

Atlas Canonical Name : {20,2,5}*400
if this polytope has a name.
Group : SmallGroup(400,170)
Rank : 4
Schlafli Type : {20,2,5}
Number of vertices, edges, etc : 20, 20, 5, 5
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,2,5,2} of size 800
Vertex Figure Of :
{2,20,2,5} of size 800
{4,20,2,5} of size 1600
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,2,5}*200
4-fold quotients : {5,2,5}*100
5-fold quotients : {4,2,5}*80
10-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
2-fold covers : {40,2,5}*800, {20,2,10}*800
3-fold covers : {20,2,15}*1200, {60,2,5}*1200
4-fold covers : {80,2,5}*1600, {20,2,20}*1600, {20,4,10}*1600, {40,2,10}*1600
5-fold covers : {20,2,25}*2000, {100,2,5}*2000, {20,10,5}*2000a, {20,10,5}*2000b
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,19)(12,16)(14,17)(18,20);;
s2 := (22,23)(24,25);;
s3 := (21,22)(23,24);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope