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# Polytope of Type {5,10,2}

Atlas Canonical Name : {5,10,2}*240a
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 4
Schlafli Type : {5,10,2}
Number of vertices, edges, etc : 6, 30, 12, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,10,2,2} of size 480
{5,10,2,3} of size 720
{5,10,2,4} of size 960
{5,10,2,5} of size 1200
{5,10,2,6} of size 1440
{5,10,2,7} of size 1680
{5,10,2,8} of size 1920
Vertex Figure Of :
{2,5,10,2} of size 480
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,5,2}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,10,2}*480, {10,10,2}*480c, {10,10,2}*480d
3-fold covers : {15,10,2}*720
4-fold covers : {5,10,4}*960, {20,10,2}*960a, {20,10,2}*960b, {5,20,2}*960, {10,10,2}*960
5-fold covers : {5,10,2}*1200
6-fold covers : {5,10,6}*1440, {10,30,2}*1440b, {15,10,2}*1440, {30,10,2}*1440a, {30,10,2}*1440b
7-fold covers : {35,10,2}*1680
8-fold covers : {5,10,8}*1920, {40,10,2}*1920a, {40,10,2}*1920b, {10,10,4}*1920, {10,20,2}*1920a, {20,10,2}*1920a, {5,20,4}*1920, {10,20,2}*1920b, {20,10,2}*1920b, {10,10,2}*1920
Permutation Representation (GAP) :
```s0 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
s1 := ( 3, 5)( 4,11)( 6,12)( 7, 9);;
s2 := ( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11);;
s3 := (13,14);;
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,
s0*s1*s2*s0*s1*s2*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope