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# Polytope of Type {4,12,2}

Atlas Canonical Name : {4,12,2}*384c
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 8, 48, 24, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2,2} of size 768
{4,12,2,3} of size 1152
{4,12,2,5} of size 1920
Vertex Figure Of :
{2,4,12,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,2}*192
4-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
8-fold quotients : {4,3,2}*48, {2,6,2}*48
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,2}*768d, {4,12,4}*768h, {8,12,2}*768g, {8,12,2}*768h, {4,24,2}*768e, {4,24,2}*768f
3-fold covers : {4,36,2}*1152c, {12,12,2}*1152i, {4,12,6}*1152h, {4,12,6}*1152i, {12,12,2}*1152k
5-fold covers : {4,12,10}*1920c, {20,12,2}*1920c, {4,60,2}*1920c
Permutation Representation (GAP) :
```s0 := ( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 1, 3)( 2, 4)( 7,10)( 8, 9)(11,12);;
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*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```

to this polytope