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# Polytope of Type {6,2,12,2}

Atlas Canonical Name : {6,2,12,2}*576
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 5
Schlafli Type : {6,2,12,2}
Number of vertices, edges, etc : 6, 6, 12, 12, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,12,2,2} of size 1152
{6,2,12,2,3} of size 1728
Vertex Figure Of :
{2,6,2,12,2} of size 1152
{3,6,2,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,12,2}*288, {6,2,6,2}*288
3-fold quotients : {2,2,12,2}*192, {6,2,4,2}*192
4-fold quotients : {3,2,6,2}*144, {6,2,3,2}*144
6-fold quotients : {3,2,4,2}*96, {2,2,6,2}*96, {6,2,2,2}*96
8-fold quotients : {3,2,3,2}*72
9-fold quotients : {2,2,4,2}*64
12-fold quotients : {2,2,3,2}*48, {3,2,2,2}*48
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,2,12,4}*1152a, {6,4,12,2}*1152, {12,2,12,2}*1152, {6,2,24,2}*1152
3-fold covers : {18,2,12,2}*1728, {6,2,36,2}*1728, {6,6,12,2}*1728a, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,6,12,2}*1728e
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);;
s4 := (19,20);;
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, 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(20)!(3,4)(5,6);
s1 := Sym(20)!(1,5)(2,3)(4,6);
s2 := Sym(20)!( 8, 9)(10,11)(13,16)(14,15)(17,18);
s3 := Sym(20)!( 7,13)( 8,10)( 9,17)(11,14)(12,15)(16,18);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|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,
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