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

Atlas Canonical Name : {6,4,2,4}*384a
if this polytope has a name.
Group : SmallGroup(384,19195)
Rank : 5
Schlafli Type : {6,4,2,4}
Number of vertices, edges, etc : 6, 12, 4, 4, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,2,4,2} of size 768
{6,4,2,4,3} of size 1152
Vertex Figure Of :
{2,6,4,2,4} of size 768
{3,6,4,2,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,2,2,4}*192, {6,4,2,2}*192a
3-fold quotients : {2,4,2,4}*128
4-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
6-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
8-fold quotients : {3,2,2,2}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,4,4,4}*768, {12,4,2,4}*768a, {6,4,2,8}*768a, {6,8,2,4}*768
3-fold covers : {18,4,2,4}*1152a, {6,4,6,4}*1152a, {6,12,2,4}*1152a, {6,4,2,12}*1152a, {6,12,2,4}*1152b
5-fold covers : {30,4,2,4}*1920a, {6,4,10,4}*1920, {6,4,2,20}*1920a, {6,20,2,4}*1920a
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);;
s3 := (14,15);;
s4 := (13,14)(15,16);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope