# Polytope of Type {2,3,6,2,4}

Atlas Canonical Name : {2,3,6,2,4}*576
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 6
Schlafli Type : {2,3,6,2,4}
Number of vertices, edges, etc : 2, 3, 9, 6, 4, 4
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,6,2,4,2} of size 1152
{2,3,6,2,4,3} of size 1728
Vertex Figure Of :
{2,2,3,6,2,4} of size 1152
{3,2,3,6,2,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,6,2,2}*288
3-fold quotients : {2,3,2,2,4}*192
6-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,6,4,4}*1152, {2,3,6,2,8}*1152, {2,6,6,2,4}*1152c
3-fold covers : {2,9,6,2,4}*1728, {2,3,6,2,4}*1728, {2,3,6,2,12}*1728, {6,3,6,2,4}*1728, {2,3,6,6,4}*1728d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,10);;
s2 := ( 3, 8)( 4, 6)( 5,10)( 7, 9);;
s3 := ( 6, 7)( 8, 9)(10,11);;
s4 := (13,14);;
s5 := (12,13)(14,15);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(15)!(1,2);
s1 := Sym(15)!( 4, 5)( 6, 7)( 8,11)( 9,10);
s2 := Sym(15)!( 3, 8)( 4, 6)( 5,10)( 7, 9);
s3 := Sym(15)!( 6, 7)( 8, 9)(10,11);
s4 := Sym(15)!(13,14);
s5 := Sym(15)!(12,13)(14,15);
poly := sub<Sym(15)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;

```

to this polytope