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# Polytope of Type {4,6,2}

Atlas Canonical Name : {4,6,2}*144
if this polytope has a name.
Group : SmallGroup(144,186)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 6, 18, 9, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,2} of size 288
{4,6,2,3} of size 432
{4,6,2,4} of size 576
{4,6,2,5} of size 720
{4,6,2,6} of size 864
{4,6,2,7} of size 1008
{4,6,2,8} of size 1152
{4,6,2,9} of size 1296
{4,6,2,10} of size 1440
{4,6,2,11} of size 1584
{4,6,2,12} of size 1728
{4,6,2,13} of size 1872
Vertex Figure Of :
{2,4,6,2} of size 288
{4,4,6,2} of size 576
{6,4,6,2} of size 864
{8,4,6,2} of size 1152
{10,4,6,2} of size 1440
{12,4,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,2}*288
3-fold covers : {4,6,2}*432, {12,6,2}*432a, {12,6,2}*432b, {12,6,2}*432c
4-fold covers : {8,6,2}*576, {4,6,4}*576a, {4,12,2}*576
5-fold covers : {20,6,2}*720
6-fold covers : {4,6,2}*864a, {12,6,2}*864e, {12,6,2}*864f, {4,6,6}*864j, {4,6,2}*864b, {12,6,2}*864h, {12,6,2}*864i
7-fold covers : {28,6,2}*1008
8-fold covers : {4,12,4}*1152b, {4,24,2}*1152a, {8,12,2}*1152a, {4,24,2}*1152b, {8,12,2}*1152b, {4,12,2}*1152, {4,6,8}*1152a, {8,6,4}*1152b, {16,6,2}*1152
9-fold covers : {4,18,2}*1296, {36,6,2}*1296a, {12,6,2}*1296, {36,6,2}*1296b, {36,6,2}*1296c, {4,6,6}*1296d
10-fold covers : {4,6,10}*1440, {4,30,2}*1440, {20,6,2}*1440
11-fold covers : {44,6,2}*1584
12-fold covers : {8,6,2}*1728a, {24,6,2}*1728d, {24,6,2}*1728e, {4,6,4}*1728b, {12,6,4}*1728f, {12,6,4}*1728g, {4,12,2}*1728b, {12,12,2}*1728d, {12,12,2}*1728e, {8,6,6}*1728f, {4,6,12}*1728k, {4,12,2}*1728c, {12,12,2}*1728i, {8,6,2}*1728b, {24,6,2}*1728g, {4,12,6}*1728n, {4,6,4}*1728c, {12,6,4}*1728m, {24,6,2}*1728h, {12,6,4}*1728n, {12,12,2}*1728k, {12,12,2}*1728n
13-fold covers : {52,6,2}*1872
Permutation Representation (GAP) :
```s0 := (5,6);;
s1 := (1,2)(3,5)(4,6);;
s2 := (2,3)(5,6);;
s3 := (7,8);;
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, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;

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

```

to this polytope