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# Polytope of Type {4,3,6}

Atlas Canonical Name : {4,3,6}*144
if this polytope has a name.
Group : SmallGroup(144,183)
Rank : 4
Schlafli Type : {4,3,6}
Number of vertices, edges, etc : 4, 6, 9, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,6,2} of size 288
{4,3,6,3} of size 432
{4,3,6,4} of size 576
{4,3,6,6} of size 864
{4,3,6,6} of size 864
{4,3,6,8} of size 1152
{4,3,6,9} of size 1296
{4,3,6,3} of size 1296
{4,3,6,10} of size 1440
{4,3,6,12} of size 1728
{4,3,6,12} of size 1728
{4,3,6,4} of size 1728
Vertex Figure Of :
{2,4,3,6} of size 288
{4,4,3,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,6}*288, {4,6,6}*288e, {4,6,6}*288f
3-fold covers : {4,9,6}*432, {4,3,6}*432
4-fold covers : {4,12,6}*576e, {4,12,6}*576g, {8,3,6}*576, {4,6,12}*576e, {4,3,6}*576, {4,6,6}*576b, {4,3,12}*576
5-fold covers : {4,15,6}*720
6-fold covers : {4,9,6}*864, {4,18,6}*864d, {4,18,6}*864e, {4,3,6}*864, {4,6,6}*864d, {4,6,6}*864f, {4,6,6}*864i, {12,3,6}*864, {12,6,6}*864h
7-fold covers : {4,21,6}*1008
8-fold covers : {4,6,6}*1152b, {8,3,6}*1152, {8,6,6}*1152a, {4,24,6}*1152h, {4,24,6}*1152j, {4,12,12}*1152e, {4,12,12}*1152g, {4,6,24}*1152e, {4,3,12}*1152a, {4,12,6}*1152f, {4,6,6}*1152e, {4,12,6}*1152i, {8,6,6}*1152c, {8,6,6}*1152e, {4,6,12}*1152d, {4,3,24}*1152, {4,3,6}*1152b, {4,6,6}*1152g, {4,6,6}*1152h, {4,3,12}*1152b, {4,6,12}*1152f, {4,6,12}*1152h
9-fold covers : {4,27,6}*1296, {4,9,18}*1296, {4,3,18}*1296, {4,3,6}*1296a, {4,9,6}*1296a, {4,9,6}*1296b, {4,9,6}*1296c, {4,9,6}*1296d
10-fold covers : {4,6,30}*1440d, {20,6,6}*1440d, {4,15,6}*1440b, {4,30,6}*1440e, {4,30,6}*1440f
11-fold covers : {4,33,6}*1584
12-fold covers : {4,36,6}*1728d, {4,36,6}*1728f, {4,12,6}*1728d, {4,12,6}*1728f, {8,9,6}*1728, {8,3,6}*1728, {4,18,12}*1728d, {4,6,12}*1728e, {4,9,6}*1728, {4,3,6}*1728, {4,18,6}*1728b, {4,6,6}*1728a, {4,9,12}*1728, {4,3,12}*1728, {24,3,6}*1728, {4,12,6}*1728l, {4,12,6}*1728m, {4,6,12}*1728j, {4,6,6}*1728c, {12,6,6}*1728c, {12,6,6}*1728d
13-fold covers : {4,39,6}*1872
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s3 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope