# Polytope of Type {20,6,2}

Atlas Canonical Name : {20,6,2}*480b
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 4
Schlafli Type : {20,6,2}
Number of vertices, edges, etc : 20, 60, 6, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{20,6,2,2} of size 960
{20,6,2,3} of size 1440
{20,6,2,4} of size 1920
Vertex Figure Of :
{2,20,6,2} of size 960
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {4,6,2}*96b
10-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,6,2}*960c
3-fold covers : {20,18,2}*1440b, {20,6,6}*1440d, {60,6,2}*1440d
4-fold covers : {40,6,2}*1920a, {20,12,2}*1920b, {20,6,2}*1920a, {20,6,4}*1920b, {40,6,2}*1920b, {40,6,2}*1920c, {20,12,2}*1920c, {20,6,4}*1920c
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 4)( 5,18)( 6,17)( 7,20)( 8,19)( 9,14)(10,13)(11,16)(12,15);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,17)(10,19)(11,18)(12,20)(14,15);;
s2 := ( 3, 4)( 7, 8)(11,12)(15,16)(19,20);;
s3 := (21,22);;
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, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

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

```

to this polytope