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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,5,2,2}*480c
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 5
Schlafli Type : {6,5,2,2}
Number of vertices, edges, etc : 12, 30, 10, 2, 2
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,5,2,2,2} of size 960
{6,5,2,2,3} of size 1440
{6,5,2,2,4} of size 1920
Vertex Figure Of :
{2,6,5,2,2} of size 960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,5,2,2}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,5,2,4}*960c, {6,5,2,2}*960b, {6,10,2,2}*960c, {6,10,2,2}*960f
3-fold covers : {6,5,2,6}*1440c, {6,15,2,2}*1440
4-fold covers : {6,5,2,8}*1920c, {6,5,2,4}*1920b, {6,10,2,4}*1920c, {6,10,2,4}*1920f, {6,10,4,2}*1920b, {6,20,2,2}*1920b, {6,20,2,2}*1920c, {6,10,2,2}*1920b, {12,5,2,2}*1920
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s1 := ( 2, 3)( 4, 6)( 5, 9)( 8,11);;
s2 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
s3 := (13,14);;
s4 := (15,16);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);
s1 := Sym(16)!( 2, 3)( 4, 6)( 5, 9)( 8,11);
s2 := Sym(16)!( 2, 9)( 4,12)( 5, 7)( 6, 8);
s3 := Sym(16)!(13,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

```

to this polytope