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# Polytope of Type {3,2,12,4}

Atlas Canonical Name : {3,2,12,4}*576a
if this polytope has a name.
Group : SmallGroup(576,6139)
Rank : 5
Schlafli Type : {3,2,12,4}
Number of vertices, edges, etc : 3, 3, 12, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,12,4,2} of size 1152
Vertex Figure Of :
{2,3,2,12,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,12,2}*288, {3,2,6,4}*288a
3-fold quotients : {3,2,4,4}*192
4-fold quotients : {3,2,6,2}*144
6-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
8-fold quotients : {3,2,3,2}*72
12-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,12,8}*1152a, {3,2,24,4}*1152a, {3,2,12,8}*1152b, {3,2,24,4}*1152b, {3,2,12,4}*1152a, {6,2,12,4}*1152a
3-fold covers : {9,2,12,4}*1728a, {3,2,36,4}*1728a, {3,6,12,4}*1728a, {3,2,12,12}*1728a, {3,2,12,12}*1728c, {3,6,12,4}*1728d
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,13)(11,15)(12,14)(18,23)(19,22)(20,21)(24,25)(26,27);;
s3 := ( 4,11)( 5, 7)( 6,20)( 8,12)( 9,26)(10,14)(13,24)(15,21)(16,22)(17,18)
(19,27)(23,25);;
s4 := ( 5, 9)( 6,13)(11,18)(12,19)(14,22)(15,23);;
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,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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(27)!(2,3);
s1 := Sym(27)!(1,2);
s2 := Sym(27)!( 5, 6)( 7, 8)( 9,13)(11,15)(12,14)(18,23)(19,22)(20,21)(24,25)
(26,27);
s3 := Sym(27)!( 4,11)( 5, 7)( 6,20)( 8,12)( 9,26)(10,14)(13,24)(15,21)(16,22)
(17,18)(19,27)(23,25);
s4 := Sym(27)!( 5, 9)( 6,13)(11,18)(12,19)(14,22)(15,23);
poly := sub<Sym(27)|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, s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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