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# Polytope of Type {6,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,12}*288
if this polytope has a name.
Group : SmallGroup(288,951)
Rank : 4
Schlafli Type : {6,2,12}
Number of vertices, edges, etc : 6, 6, 12, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,12,2} of size 576
{6,2,12,4} of size 1152
{6,2,12,4} of size 1152
{6,2,12,4} of size 1152
{6,2,12,3} of size 1152
{6,2,12,6} of size 1728
{6,2,12,6} of size 1728
{6,2,12,6} of size 1728
{6,2,12,3} of size 1728
{6,2,12,6} of size 1728
Vertex Figure Of :
{2,6,2,12} of size 576
{3,6,2,12} of size 864
{4,6,2,12} of size 1152
{3,6,2,12} of size 1152
{4,6,2,12} of size 1152
{4,6,2,12} of size 1152
{4,6,2,12} of size 1728
{6,6,2,12} of size 1728
{6,6,2,12} of size 1728
{6,6,2,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,12}*144, {6,2,6}*144
3-fold quotients : {2,2,12}*96, {6,2,4}*96
4-fold quotients : {3,2,6}*72, {6,2,3}*72
6-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
8-fold quotients : {3,2,3}*36
9-fold quotients : {2,2,4}*32
12-fold quotients : {2,2,3}*24, {3,2,2}*24
18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,12}*576, {6,4,12}*576, {6,2,24}*576
3-fold covers : {6,2,36}*864, {18,2,12}*864, {6,6,12}*864a, {6,6,12}*864b, {6,6,12}*864c, {6,6,12}*864e
4-fold covers : {12,4,12}*1152, {6,8,12}*1152a, {6,4,24}*1152a, {6,8,12}*1152b, {6,4,24}*1152b, {6,4,12}*1152a, {12,2,24}*1152, {24,2,12}*1152, {6,2,48}*1152, {6,4,12}*1152b, {6,4,12}*1152c
5-fold covers : {6,10,12}*1440, {30,2,12}*1440, {6,2,60}*1440
6-fold covers : {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {18,4,12}*1728, {6,4,36}*1728, {6,12,12}*1728a, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e, {12,6,12}*1728b, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728g
Permutation Representation (GAP) :
```s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(13,16)(14,15)(17,18);;
s3 := ( 7,13)( 8,10)( 9,17)(11,14)(12,15)(16,18);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!(3,4)(5,6);
s1 := Sym(18)!(1,5)(2,3)(4,6);
s2 := Sym(18)!( 8, 9)(10,11)(13,16)(14,15)(17,18);
s3 := Sym(18)!( 7,13)( 8,10)( 9,17)(11,14)(12,15)(16,18);
poly := sub<Sym(18)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope