# Polytope of Type {4,12,6}

Atlas Canonical Name : {4,12,6}*576h
if this polytope has a name.
Group : SmallGroup(576,8653)
Rank : 4
Schlafli Type : {4,12,6}
Number of vertices, edges, etc : 4, 24, 36, 6
Order of s0s1s2s3 : 3
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,6,2} of size 1152
Vertex Figure Of :
{2,4,12,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,6}*1152k, {4,12,6}*1152l
3-fold covers : {4,12,18}*1728e, {4,36,6}*1728g, {4,12,6}*1728k
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16);;
s1 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7, 9)( 8,10)(13,15)(14,16);;
s2 := ( 2, 3)( 5,13)( 6,15)( 7,14)( 8,16)(10,11);;
s3 := ( 2, 4)( 6, 8)(10,12)(14,16);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope