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

Atlas Canonical Name : {4,6,2,3}*288a
if this polytope has a name.
Group : SmallGroup(288,958)
Rank : 5
Schlafli Type : {4,6,2,3}
Number of vertices, edges, etc : 4, 12, 6, 3, 3
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,3,2} of size 576
{4,6,2,3,3} of size 1152
{4,6,2,3,4} of size 1152
{4,6,2,3,6} of size 1728
Vertex Figure Of :
{2,4,6,2,3} of size 576
{4,4,6,2,3} of size 1152
{6,4,6,2,3} of size 1728
{3,4,6,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,2,3}*144
3-fold quotients : {4,2,2,3}*96
4-fold quotients : {2,3,2,3}*72
6-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,2,3}*576a, {8,6,2,3}*576, {4,6,2,6}*576a
3-fold covers : {4,6,2,9}*864a, {4,18,2,3}*864a, {4,6,6,3}*864a, {12,6,2,3}*864a, {12,6,2,3}*864c, {4,6,6,3}*864d
4-fold covers : {8,12,2,3}*1152a, {4,24,2,3}*1152a, {8,12,2,3}*1152b, {4,24,2,3}*1152b, {4,12,2,3}*1152a, {16,6,2,3}*1152, {4,12,2,6}*1152a, {4,6,4,6}*1152a, {4,6,2,12}*1152a, {8,6,2,6}*1152, {4,6,4,3}*1152a, {4,6,2,3}*1152b
5-fold covers : {20,6,2,3}*1440a, {4,6,2,15}*1440a, {4,30,2,3}*1440a
6-fold covers : {4,12,2,9}*1728a, {4,36,2,3}*1728a, {4,12,6,3}*1728a, {8,6,2,9}*1728, {8,18,2,3}*1728, {8,6,6,3}*1728a, {4,6,2,18}*1728a, {4,18,2,6}*1728a, {4,6,6,6}*1728a, {24,6,2,3}*1728a, {12,12,2,3}*1728a, {12,12,2,3}*1728b, {24,6,2,3}*1728c, {8,6,6,3}*1728b, {4,12,6,3}*1728d, {12,6,2,6}*1728a, {4,6,6,6}*1728d, {4,6,6,6}*1728f, {12,6,2,6}*1728c, {4,6,6,6}*1728i
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 6, 9)( 7,10);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);;
s2 := ( 1, 3)( 2, 6)( 5, 9)( 8,11);;
s3 := (14,15);;
s4 := (13,14);;
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,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope