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

Atlas Canonical Name : {5,5,2,2}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 5
Schlafli Type : {5,5,2,2}
Number of vertices, edges, etc : 6, 15, 6, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,5,2,2,2} of size 480
{5,5,2,2,3} of size 720
{5,5,2,2,4} of size 960
{5,5,2,2,5} of size 1200
{5,5,2,2,6} of size 1440
{5,5,2,2,7} of size 1680
{5,5,2,2,8} of size 1920
Vertex Figure Of :
{2,5,5,2,2} of size 480
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,5,2,4}*480, {5,5,2,2}*480, {5,10,2,2}*480a, {5,10,2,2}*480b, {10,5,2,2}*480a, {10,5,2,2}*480b
3-fold covers : {5,5,2,6}*720
4-fold covers : {5,5,2,8}*960, {5,5,2,4}*960, {5,10,2,4}*960a, {5,10,2,4}*960b, {5,10,4,2}*960, {10,5,2,4}*960a, {10,5,2,4}*960b, {5,10,2,2}*960, {10,5,2,2}*960, {10,10,2,2}*960a, {10,10,2,2}*960b, {10,10,2,2}*960c, {10,10,2,2}*960d
5-fold covers : {5,5,2,10}*1200
6-fold covers : {5,5,2,12}*1440, {5,5,2,6}*1440, {5,10,2,6}*1440a, {5,10,2,6}*1440b, {5,10,6,2}*1440, {10,5,2,6}*1440a, {10,5,2,6}*1440b, {10,15,2,2}*1440, {15,10,2,2}*1440
7-fold covers : {5,5,2,14}*1680
8-fold covers : {5,5,2,16}*1920, {5,10,4,4}*1920, {5,5,2,8}*1920, {5,10,2,8}*1920a, {5,10,2,8}*1920b, {5,10,8,2}*1920, {10,5,2,8}*1920a, {10,5,2,8}*1920b, {5,10,2,4}*1920, {5,10,4,2}*1920, {10,5,2,4}*1920, {10,10,2,4}*1920a, {10,10,2,4}*1920b, {10,10,2,4}*1920c, {10,10,2,4}*1920d, {10,10,4,2}*1920a, {10,10,4,2}*1920b, {10,20,2,2}*1920a, {10,20,2,2}*1920b, {20,10,2,2}*1920a, {20,10,2,2}*1920b, {10,10,2,2}*1920, {5,20,2,2}*1920, {20,5,2,2}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,4)(3,5);;
s3 := (6,7);;
s4 := (8,9);;
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*s2*s0*s1*s2*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope