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# Polytope of Type {2,6,5}

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

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

```

to this polytope