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

Atlas Canonical Name : {3,2,2,6}*144
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 5
Schlafli Type : {3,2,2,6}
Number of vertices, edges, etc : 3, 3, 2, 6, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,6,2} of size 288
{3,2,2,6,3} of size 432
{3,2,2,6,4} of size 576
{3,2,2,6,3} of size 576
{3,2,2,6,4} of size 576
{3,2,2,6,4} of size 576
{3,2,2,6,4} of size 864
{3,2,2,6,6} of size 864
{3,2,2,6,6} of size 864
{3,2,2,6,6} of size 864
{3,2,2,6,8} of size 1152
{3,2,2,6,4} of size 1152
{3,2,2,6,6} of size 1152
{3,2,2,6,9} of size 1296
{3,2,2,6,3} of size 1296
{3,2,2,6,6} of size 1296
{3,2,2,6,4} of size 1440
{3,2,2,6,5} of size 1440
{3,2,2,6,6} of size 1440
{3,2,2,6,5} of size 1440
{3,2,2,6,5} of size 1440
{3,2,2,6,10} of size 1440
{3,2,2,6,12} of size 1728
{3,2,2,6,12} of size 1728
{3,2,2,6,12} of size 1728
{3,2,2,6,3} of size 1728
{3,2,2,6,12} of size 1728
{3,2,2,6,4} of size 1728
Vertex Figure Of :
{2,3,2,2,6} of size 288
{3,3,2,2,6} of size 576
{4,3,2,2,6} of size 576
{6,3,2,2,6} of size 864
{4,3,2,2,6} of size 1152
{6,3,2,2,6} of size 1152
{5,3,2,2,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,3}*72
3-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,2,12}*288, {3,2,4,6}*288a, {6,2,2,6}*288
3-fold covers : {3,2,2,18}*432, {9,2,2,6}*432, {3,2,6,6}*432a, {3,2,6,6}*432b, {3,6,2,6}*432
4-fold covers : {3,2,4,12}*576a, {3,2,2,24}*576, {3,2,8,6}*576, {6,2,2,12}*576, {12,2,2,6}*576, {6,2,4,6}*576a, {6,4,2,6}*576a, {3,2,4,6}*576, {3,4,2,6}*576
5-fold covers : {3,2,10,6}*720, {3,2,2,30}*720, {15,2,2,6}*720
6-fold covers : {3,2,2,36}*864, {9,2,2,12}*864, {3,2,4,18}*864a, {9,2,4,6}*864a, {6,2,2,18}*864, {18,2,2,6}*864, {3,2,6,12}*864a, {3,2,6,12}*864b, {3,2,12,6}*864a, {3,6,2,12}*864, {3,6,4,6}*864, {3,2,12,6}*864c, {6,2,6,6}*864a, {6,2,6,6}*864b, {6,6,2,6}*864a, {6,6,2,6}*864c
7-fold covers : {3,2,14,6}*1008, {3,2,2,42}*1008, {21,2,2,6}*1008
8-fold covers : {3,2,8,12}*1152a, {3,2,4,24}*1152a, {3,2,8,12}*1152b, {3,2,4,24}*1152b, {3,2,4,12}*1152a, {3,2,16,6}*1152, {3,2,2,48}*1152, {6,4,4,6}*1152, {6,2,4,12}*1152a, {12,4,2,6}*1152a, {6,4,2,12}*1152a, {12,2,4,6}*1152a, {12,2,2,12}*1152, {6,2,8,6}*1152, {6,8,2,6}*1152, {6,2,2,24}*1152, {24,2,2,6}*1152, {3,2,4,12}*1152b, {3,4,2,12}*1152, {3,4,4,6}*1152b, {3,2,4,6}*1152b, {3,2,4,12}*1152c, {3,2,8,6}*1152b, {3,8,2,6}*1152, {3,2,8,6}*1152c, {6,2,4,6}*1152, {6,4,2,6}*1152
9-fold covers : {9,2,2,18}*1296, {3,2,2,54}*1296, {27,2,2,6}*1296, {3,2,6,18}*1296a, {3,2,6,18}*1296b, {3,2,18,6}*1296a, {3,6,2,18}*1296, {9,2,6,6}*1296a, {9,2,6,6}*1296b, {9,6,2,6}*1296, {3,6,6,6}*1296a, {3,2,6,6}*1296a, {3,2,6,6}*1296b, {3,6,2,6}*1296, {3,6,6,6}*1296c, {3,2,6,6}*1296d, {3,6,6,6}*1296e
10-fold covers : {3,2,10,12}*1440, {3,2,20,6}*1440a, {15,2,2,12}*1440, {3,2,2,60}*1440, {3,2,4,30}*1440a, {15,2,4,6}*1440a, {6,2,10,6}*1440, {6,10,2,6}*1440, {6,2,2,30}*1440, {30,2,2,6}*1440
11-fold covers : {3,2,22,6}*1584, {3,2,2,66}*1584, {33,2,2,6}*1584
12-fold covers : {9,2,4,12}*1728a, {3,2,4,36}*1728a, {3,2,2,72}*1728, {9,2,2,24}*1728, {3,2,8,18}*1728, {9,2,8,6}*1728, {12,2,2,18}*1728, {18,2,2,12}*1728, {6,2,2,36}*1728, {36,2,2,6}*1728, {6,2,4,18}*1728a, {6,4,2,18}*1728a, {18,2,4,6}*1728a, {18,4,2,6}*1728a, {3,2,6,24}*1728a, {3,2,6,24}*1728b, {3,2,24,6}*1728a, {3,6,2,24}*1728, {3,2,12,12}*1728a, {3,2,12,12}*1728b, {3,6,4,12}*1728, {3,6,8,6}*1728, {3,2,24,6}*1728c, {3,4,2,18}*1728, {9,2,4,6}*1728, {3,2,4,18}*1728, {9,4,2,6}*1728, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,2,12,6}*1728a, {6,6,2,12}*1728a, {6,6,2,12}*1728c, {6,12,2,6}*1728a, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {6,4,6,6}*1728a, {6,6,4,6}*1728a, {6,4,6,6}*1728c, {6,6,4,6}*1728c, {6,2,12,6}*1728c, {6,12,2,6}*1728c, {3,4,6,6}*1728a, {3,4,6,6}*1728b, {3,6,4,6}*1728b, {3,2,6,6}*1728a, {3,2,6,12}*1728a, {3,2,12,6}*1728a, {3,2,12,6}*1728b, {3,6,2,6}*1728, {3,12,2,6}*1728
13-fold covers : {3,2,26,6}*1872, {3,2,2,78}*1872, {39,2,2,6}*1872
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 8, 9)(10,11);;
s4 := ( 6,10)( 7, 8)( 9,11);;
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,
s1*s2*s1*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, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope