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# Polytope of Type {2,2,5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,10}*480a
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 5
Schlafli Type : {2,2,5,10}
Number of vertices, edges, etc : 2, 2, 6, 30, 12
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,5,10,2} of size 960
Vertex Figure Of :
{2,2,2,5,10} of size 960
{3,2,2,5,10} of size 1440
{4,2,2,5,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,5,5}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,5,10}*960a, {2,2,5,10}*960, {2,2,10,10}*960c, {2,2,10,10}*960d
3-fold covers : {2,2,15,10}*1440, {6,2,5,10}*1440a
4-fold covers : {8,2,5,10}*1920a, {2,2,20,10}*1920a, {2,2,20,10}*1920b, {2,4,10,10}*1920b, {4,2,5,10}*1920, {4,2,10,10}*1920c, {4,2,10,10}*1920d, {2,2,10,10}*1920, {2,2,5,20}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,13)( 8,16)( 9,11)(10,12);;
s3 := ( 7, 9)( 8,15)(10,16)(11,13);;
s4 := ( 5, 7)( 6,12)( 8,16)( 9,11)(10,13)(14,15);;
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*s1*s0*s1,
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*s2*s3*s4*s2*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope