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# Polytope of Type {5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5}*160
Also Known As : {5,5}4if this polytope has another name.
Group : SmallGroup(160,234)
Rank : 3
Schlafli Type : {5,5}
Number of vertices, edges, etc : 16, 40, 16
Order of s0s1s2 : 4
Order of s0s1s2s1 : 5
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{5,5,2} of size 320
Vertex Figure Of :
{2,5,5} of size 320
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,5}*320, {5,10}*320a, {10,5}*320a, {5,10}*320b, {10,5}*320b
4-fold covers : {5,10}*640, {10,5}*640, {10,10}*640a, {10,10}*640b, {10,10}*640c, {5,20}*640a, {5,20}*640b, {20,5}*640a, {20,5}*640b, {10,10}*640d
6-fold covers : {10,15}*960, {15,10}*960
8-fold covers : {5,20}*1280, {10,20}*1280a, {10,20}*1280b, {20,5}*1280, {20,10}*1280a, {20,10}*1280b, {10,20}*1280c, {20,10}*1280c, {10,10}*1280a, {10,20}*1280d, {10,20}*1280e, {20,10}*1280d, {20,10}*1280e, {10,10}*1280b, {10,10}*1280c, {10,20}*1280f, {20,10}*1280f
10-fold covers : {5,10}*1600, {10,5}*1600
12-fold covers : {15,20}*1920a, {15,20}*1920b, {20,15}*1920a, {20,15}*1920b, {10,15}*1920, {10,30}*1920a, {15,10}*1920, {30,10}*1920a, {15,15}*1920, {10,30}*1920b, {30,10}*1920b
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14);;
s1 := ( 2, 9)( 3,12)( 5,15)( 6, 7)( 8,14)(13,16);;
s2 := ( 1, 2)( 7, 8)( 9,15)(10,16)(11,14)(12,13);;
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*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope