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

Atlas Canonical Name : {5,6,2,2}*480c
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 5
Schlafli Type : {5,6,2,2}
Number of vertices, edges, etc : 10, 30, 12, 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 :
{5,6,2,2,2} of size 960
{5,6,2,2,3} of size 1440
{5,6,2,2,4} of size 1920
Vertex Figure Of :
{2,5,6,2,2} of size 960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,3,2,2}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,6,2,4}*960c, {5,6,4,2}*960b, {5,6,2,2}*960b, {10,6,2,2}*960c, {10,6,2,2}*960d
3-fold covers : {5,6,2,6}*1440c, {5,6,6,2}*1440b
4-fold covers : {5,6,4,4}*1920b, {5,6,2,8}*1920c, {5,6,8,2}*1920b, {5,6,2,4}*1920b, {5,6,4,2}*1920b, {10,6,2,4}*1920c, {10,6,2,4}*1920d, {10,6,4,2}*1920d, {10,6,4,2}*1920e, {10,12,2,2}*1920c, {10,12,2,2}*1920d, {10,6,2,2}*1920b, {5,12,2,2}*1920
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s1 := ( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);;
s2 := ( 1, 3)( 2, 6)( 8, 9)(10,11);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);
s1 := Sym(16)!( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12);
s2 := Sym(16)!( 1, 3)( 2, 6)( 8, 9)(10,11);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0 >;

```

to this polytope