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# Polytope of Type {12,2,12}

Atlas Canonical Name : {12,2,12}*576
if this polytope has a name.
Group : SmallGroup(576,5884)
Rank : 4
Schlafli Type : {12,2,12}
Number of vertices, edges, etc : 12, 12, 12, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,2,12,2} of size 1152
Vertex Figure Of :
{2,12,2,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,2,12}*288, {12,2,6}*288
3-fold quotients : {4,2,12}*192, {12,2,4}*192
4-fold quotients : {3,2,12}*144, {12,2,3}*144, {6,2,6}*144
6-fold quotients : {2,2,12}*96, {12,2,2}*96, {4,2,6}*96, {6,2,4}*96
8-fold quotients : {3,2,6}*72, {6,2,3}*72
9-fold quotients : {4,2,4}*64
12-fold quotients : {3,2,4}*48, {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
16-fold quotients : {3,2,3}*36
18-fold quotients : {2,2,4}*32, {4,2,2}*32
24-fold quotients : {2,2,3}*24, {3,2,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,12}*1152, {12,2,24}*1152, {24,2,12}*1152
3-fold covers : {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {12,6,12}*1728b, {12,6,12}*1728e, {12,6,12}*1728f
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)(16,17)(19,22)(20,21)(23,24);;
s3 := (13,19)(14,16)(15,23)(17,20)(18,21)(22,24);;
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*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(24)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(24)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(24)!(14,15)(16,17)(19,22)(20,21)(23,24);
s3 := Sym(24)!(13,19)(14,16)(15,23)(17,20)(18,21)(22,24);
poly := sub<Sym(24)|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*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