# Polytope of Type {10,10}

Atlas Canonical Name : {10,10}*480
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 3
Schlafli Type : {10,10}
Number of vertices, edges, etc : 24, 120, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{10,10,2} of size 960
{10,10,4} of size 1920
Vertex Figure Of :
{2,10,10} of size 960
{4,10,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
4-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
8-fold quotients : {5,5}*60
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,20}*960a, {20,10}*960a, {10,20}*960b, {20,10}*960b, {10,10}*960
3-fold covers : {10,30}*1440, {30,10}*1440
4-fold covers : {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
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 8, 9)(10,11);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,10);;
s2 := ( 1, 2)( 8,10)( 9,11);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope