# Polytope of Type {12,2,3,2,2}

Atlas Canonical Name : {12,2,3,2,2}*576
if this polytope has a name.
Group : SmallGroup(576,8545)
Rank : 6
Schlafli Type : {12,2,3,2,2}
Number of vertices, edges, etc : 12, 12, 3, 3, 2, 2
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,2,3,2,2,2} of size 1152
{12,2,3,2,2,3} of size 1728
Vertex Figure Of :
{2,12,2,3,2,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,2,3,2,2}*288
3-fold quotients : {4,2,3,2,2}*192
4-fold quotients : {3,2,3,2,2}*144
6-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,3,2,4}*1152, {24,2,3,2,2}*1152, {12,2,6,2,2}*1152
3-fold covers : {12,2,9,2,2}*1728, {36,2,3,2,2}*1728, {12,6,3,2,2}*1728a, {12,2,3,2,6}*1728, {12,2,3,6,2}*1728, {12,6,3,2,2}*1728b
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,15);;
s3 := (13,14);;
s4 := (16,17);;
s5 := (18,19);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(19)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(19)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(19)!(14,15);
s3 := Sym(19)!(13,14);
s4 := Sym(19)!(16,17);
s5 := Sym(19)!(18,19);
poly := sub<Sym(19)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope