# Polytope of Type {4,6,2,10}

Atlas Canonical Name : {4,6,2,10}*960a
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 5
Schlafli Type : {4,6,2,10}
Number of vertices, edges, etc : 4, 12, 6, 10, 10
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,10,2} of size 1920
Vertex Figure Of :
{2,4,6,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,2,5}*480a, {2,6,2,10}*480
3-fold quotients : {4,2,2,10}*320
4-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
5-fold quotients : {4,6,2,2}*192a
6-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
8-fold quotients : {2,3,2,5}*120
10-fold quotients : {2,6,2,2}*96
12-fold quotients : {2,2,2,5}*80
15-fold quotients : {4,2,2,2}*64
20-fold quotients : {2,3,2,2}*48
30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,2,10}*1920a, {4,6,4,10}*1920a, {4,6,2,20}*1920a, {8,6,2,10}*1920
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 6, 9)( 7,10);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);;
s2 := ( 1, 3)( 2, 6)( 5, 9)( 8,11);;
s3 := (15,16)(17,18)(19,20)(21,22);;
s4 := (13,17)(14,15)(16,21)(18,19)(20,22);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(22)!( 2, 5)( 6, 9)( 7,10);
s1 := Sym(22)!( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);
s2 := Sym(22)!( 1, 3)( 2, 6)( 5, 9)( 8,11);
s3 := Sym(22)!(15,16)(17,18)(19,20)(21,22);
s4 := Sym(22)!(13,17)(14,15)(16,21)(18,19)(20,22);
poly := sub<Sym(22)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope