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

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

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

```

to this polytope