# Polytope of Type {5,2,6,3}

Atlas Canonical Name : {5,2,6,3}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 5
Schlafli Type : {5,2,6,3}
Number of vertices, edges, etc : 5, 5, 8, 12, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,6,3,2} of size 960
Vertex Figure Of :
{2,5,2,6,3} of size 960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2,3,3}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,12,3}*960, {5,2,6,6}*960, {10,2,6,3}*960
3-fold covers : {5,2,6,3}*1440, {15,2,6,3}*1440
4-fold covers : {5,2,6,3}*1920, {20,2,6,3}*1920, {10,4,6,3}*1920, {5,2,6,12}*1920a, {5,2,12,6}*1920a, {5,2,6,12}*1920b, {5,2,12,6}*1920b, {10,2,12,3}*1920, {5,2,6,6}*1920b, {10,2,6,6}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 6, 9)( 7,11);;
s3 := ( 6, 7)( 8, 9)(10,11);;
s4 := ( 6, 9)( 7,11)( 8,10);;
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,
s1*s2*s1*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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(2,3)(4,5);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!( 6, 9)( 7,11);
s3 := Sym(11)!( 6, 7)( 8, 9)(10,11);
s4 := Sym(11)!( 6, 9)( 7,11)( 8,10);
poly := sub<Sym(11)|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, s1*s2*s1*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*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope