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

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

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

```

to this polytope