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# Polytope of Type {5,5}

Atlas Canonical Name : {5,5}*60
Also Known As : {5,5}3if this polytope has another name.
Group : SmallGroup(60,5)
Rank : 3
Schlafli Type : {5,5}
Number of vertices, edges, etc : 6, 15, 6
Order of s0s1s2 : 3
Order of s0s1s2s1 : 3
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{5,5,2} of size 120
{5,5,4} of size 1920
Vertex Figure Of :
{2,5,5} of size 120
{4,5,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
4-fold covers : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
6-fold covers : {10,15}*360, {15,10}*360
8-fold covers : {10,20}*480a, {10,20}*480b, {20,10}*480a, {20,10}*480b, {5,20}*480, {20,5}*480, {10,10}*480
10-fold covers : {5,5}*600, {5,10}*600, {10,5}*600
12-fold covers : {10,15}*720, {10,30}*720a, {10,30}*720b, {15,10}*720, {30,10}*720a, {30,10}*720b
14-fold covers : {10,35}*840, {35,10}*840
16-fold covers : {10,40}*960a, {10,40}*960b, {40,10}*960a, {40,10}*960b, {10,20}*960a, {20,10}*960a, {10,20}*960b, {20,10}*960b, {10,10}*960, {5,5}*960
18-fold covers : {10,45}*1080, {45,10}*1080
20-fold covers : {5,10}*1200a, {5,10}*1200b, {10,5}*1200a, {10,5}*1200b, {10,10}*1200a, {10,10}*1200b, {10,10}*1200c, {10,10}*1200d
22-fold covers : {10,55}*1320, {55,10}*1320
24-fold covers : {10,60}*1440a, {10,60}*1440b, {60,10}*1440a, {60,10}*1440b, {15,20}*1440a, {20,15}*1440a, {15,15}*1440, {15,20}*1440b, {20,15}*1440b, {10,30}*1440, {30,10}*1440
26-fold covers : {10,65}*1560, {65,10}*1560
28-fold covers : {10,35}*1680, {10,70}*1680a, {10,70}*1680b, {35,10}*1680, {70,10}*1680a, {70,10}*1680b
30-fold covers : {10,15}*1800a, {15,10}*1800b
32-fold covers : {10,80}*1920a, {10,80}*1920b, {80,10}*1920a, {80,10}*1920b, {20,20}*1920a, {10,40}*1920a, {40,10}*1920a, {10,20}*1920, {20,10}*1920, {20,20}*1920b, {20,20}*1920c, {20,20}*1920d, {10,40}*1920b, {40,10}*1920b, {10,10}*1920, {5,5}*1920a, {5,10}*1920a, {5,10}*1920b, {10,5}*1920a, {10,5}*1920b, {5,5}*1920b, {5,5}*1920c, {5,10}*1920c, {5,10}*1920d, {10,5}*1920c, {10,5}*1920d
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,4)(3,5);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(5)!(2,3)(4,5);
s1 := Sym(5)!(1,2)(3,4);
s2 := Sym(5)!(2,4)(3,5);
poly := sub<Sym(5)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, 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 >;

```
References : None.
to this polytope