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

Atlas Canonical Name : {2,2,6,3}*144
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 5
Schlafli Type : {2,2,6,3}
Number of vertices, edges, etc : 2, 2, 6, 9, 3
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,6,3,2} of size 288
{2,2,6,3,4} of size 576
{2,2,6,3,6} of size 864
{2,2,6,3,4} of size 1152
Vertex Figure Of :
{2,2,2,6,3} of size 288
{3,2,2,6,3} of size 432
{4,2,2,6,3} of size 576
{5,2,2,6,3} of size 720
{6,2,2,6,3} of size 864
{7,2,2,6,3} of size 1008
{8,2,2,6,3} of size 1152
{9,2,2,6,3} of size 1296
{10,2,2,6,3} of size 1440
{11,2,2,6,3} of size 1584
{12,2,2,6,3} of size 1728
{13,2,2,6,3} of size 1872
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,6,3}*288, {2,4,6,3}*288, {2,2,6,6}*288b
3-fold covers : {2,2,6,9}*432, {2,2,6,3}*432, {2,6,6,3}*432b, {6,2,6,3}*432
4-fold covers : {8,2,6,3}*576, {2,8,6,3}*576, {4,4,6,3}*576, {2,2,6,12}*576b, {4,2,6,6}*576b, {2,2,12,6}*576c, {2,4,6,6}*576c, {2,2,6,3}*576, {2,2,12,3}*576
5-fold covers : {2,10,6,3}*720, {10,2,6,3}*720, {2,2,6,15}*720
6-fold covers : {4,2,6,9}*864, {4,2,6,3}*864, {2,4,6,9}*864, {2,4,6,3}*864a, {2,2,6,18}*864b, {2,2,6,6}*864a, {12,2,6,3}*864, {2,12,6,3}*864b, {6,4,6,3}*864, {4,6,6,3}*864d, {2,2,6,6}*864d, {2,6,6,6}*864c, {6,2,6,6}*864b
7-fold covers : {2,14,6,3}*1008, {14,2,6,3}*1008, {2,2,6,21}*1008
8-fold covers : {8,4,6,3}*1152a, {4,8,6,3}*1152a, {8,4,6,3}*1152b, {4,8,6,3}*1152b, {4,4,6,3}*1152, {16,2,6,3}*1152, {2,16,6,3}*1152, {4,4,6,6}*1152c, {2,4,12,6}*1152c, {2,2,12,12}*1152b, {4,2,12,6}*1152a, {4,2,6,12}*1152c, {2,4,6,12}*1152c, {8,2,6,6}*1152b, {2,2,24,6}*1152a, {2,8,6,6}*1152c, {2,2,6,24}*1152c, {4,2,6,3}*1152, {4,2,12,3}*1152, {2,2,12,3}*1152, {2,2,24,3}*1152, {2,4,6,3}*1152a, {2,4,12,3}*1152, {2,2,6,6}*1152a, {2,2,12,6}*1152b
9-fold covers : {2,2,18,9}*1296, {2,2,6,9}*1296a, {2,2,6,27}*1296, {2,2,6,9}*1296b, {2,2,6,9}*1296c, {2,2,6,9}*1296d, {2,2,6,3}*1296, {2,2,18,3}*1296, {2,6,6,9}*1296b, {2,18,6,3}*1296b, {6,2,6,9}*1296, {18,2,6,3}*1296, {2,6,6,3}*1296c, {2,6,6,3}*1296d, {2,6,6,3}*1296e, {6,2,6,3}*1296, {6,6,6,3}*1296c, {6,6,6,3}*1296d, {6,6,6,3}*1296e
10-fold covers : {20,2,6,3}*1440, {2,20,6,3}*1440, {10,4,6,3}*1440, {4,10,6,3}*1440, {4,2,6,15}*1440, {2,4,6,15}*1440, {2,2,30,6}*1440a, {2,10,6,6}*1440b, {10,2,6,6}*1440b, {2,2,6,30}*1440c
11-fold covers : {2,22,6,3}*1584, {22,2,6,3}*1584, {2,2,6,33}*1584
12-fold covers : {8,2,6,9}*1728, {8,2,6,3}*1728, {2,8,6,9}*1728, {4,4,6,9}*1728, {2,8,6,3}*1728a, {4,4,6,3}*1728a, {2,2,6,36}*1728b, {2,2,6,12}*1728a, {4,2,6,18}*1728b, {4,2,6,6}*1728a, {2,2,12,18}*1728b, {2,4,6,18}*1728b, {2,2,12,6}*1728c, {2,4,6,6}*1728c, {24,2,6,3}*1728, {2,24,6,3}*1728b, {12,4,6,3}*1728, {6,8,6,3}*1728, {8,6,6,3}*1728b, {4,12,6,3}*1728d, {2,2,6,9}*1728, {2,2,12,9}*1728, {2,2,6,3}*1728, {2,2,12,3}*1728, {2,6,6,12}*1728c, {6,2,6,12}*1728b, {12,2,6,6}*1728b, {4,2,6,6}*1728d, {2,2,6,12}*1728g, {2,2,12,6}*1728g, {2,12,6,6}*1728e, {6,4,6,6}*1728c, {2,4,6,6}*1728h, {2,6,12,6}*1728g, {6,2,12,6}*1728c, {4,6,6,6}*1728i, {4,6,6,3}*1728b, {6,4,6,3}*1728b, {6,6,6,3}*1728d, {2,6,6,3}*1728, {2,6,12,3}*1728b, {6,2,6,3}*1728, {6,2,12,3}*1728
13-fold covers : {2,26,6,3}*1872, {26,2,6,3}*1872, {2,2,6,39}*1872
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 8, 9)(10,11)(12,13);;
s3 := ( 5, 8)( 6,12)( 7,10)(11,13);;
s4 := ( 5, 6)( 8,11)( 9,10)(12,13);;
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*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope