# Polytope of Type {10,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,2}*960
if this polytope has a name.
Group : SmallGroup(960,11356)
Rank : 4
Schlafli Type : {10,10,2}
Number of vertices, edges, etc : 24, 120, 24, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,10,2,2} of size 1920
Vertex Figure Of :
{2,10,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10,2}*480, {10,5,2}*480, {10,10,2}*480a, {10,10,2}*480b, {10,10,2}*480c, {10,10,2}*480d
4-fold quotients : {5,5,2}*240, {5,10,2}*240a, {5,10,2}*240b, {10,5,2}*240a, {10,5,2}*240b
8-fold quotients : {5,5,2}*120
60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,10,4}*1920, {10,20,2}*1920a, {20,10,2}*1920a, {10,20,2}*1920b, {20,10,2}*1920b, {10,10,2}*1920
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);;
s3 := (12,13);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
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(13)!( 3, 4)( 5, 6)( 8, 9)(10,11);
s1 := Sym(13)!( 3, 5)( 4, 6)( 7, 8)( 9,10);
s2 := Sym(13)!( 1, 2)( 8,10)( 9,11);
s3 := Sym(13)!(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, 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 >;

```

to this polytope