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

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

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

```

to this polytope