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# Polytope of Type {2,12,6}

Atlas Canonical Name : {2,12,6}*384a
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 16, 48, 8
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,6,2} of size 768
{2,12,6,3} of size 1920
Vertex Figure Of :
{2,2,12,6} of size 768
{3,2,12,6} of size 1152
{5,2,12,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,6}*192
4-fold quotients : {2,3,6}*96, {2,6,3}*96
8-fold quotients : {2,3,3}*48
12-fold quotients : {2,4,2}*32
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,12}*768a, {4,12,6}*768a, {2,12,6}*768, {2,12,12}*768d, {2,24,6}*768a, {2,24,6}*768b
3-fold covers : {2,12,6}*1152a, {6,12,6}*1152a, {2,12,6}*1152e
5-fold covers : {2,60,6}*1920a, {10,12,6}*1920a, {2,12,30}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3, 7)( 4, 8)( 9,14)(10,13)(11,12);;
s2 := ( 3, 9)( 4,10)( 5,13)( 6,14)( 7,11)( 8,12);;
s3 := ( 3, 7)( 4, 8)( 5, 6)( 9,13)(10,14)(11,12);;
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,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope