Polytope of Type {2,6,6,4}

Atlas Canonical Name : {2,6,6,4}*576b
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 5
Schlafli Type : {2,6,6,4}
Number of vertices, edges, etc : 2, 6, 18, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,6,4,2} of size 1152
Vertex Figure Of :
{2,2,6,6,4} of size 1152
{3,2,6,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,6,2}*288b
3-fold quotients : {2,2,6,4}*192a
4-fold quotients : {2,6,3,2}*144
6-fold quotients : {2,2,6,2}*96
9-fold quotients : {2,2,2,4}*64
12-fold quotients : {2,2,3,2}*48
18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,12,4}*1152b, {4,6,6,4}*1152c, {2,12,6,4}*1152a, {2,6,6,8}*1152b
3-fold covers : {2,6,18,4}*1728b, {2,6,6,4}*1728a, {2,6,6,12}*1728d, {6,6,6,4}*1728e, {2,6,6,4}*1728h, {2,6,6,12}*1728g
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)
(34,37)(35,38);;
s2 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)
(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);;
s3 := ( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,31)(22,30)
(23,32)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35);;
s4 := ( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)(12,30)
(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)
(33,36)(34,37)(35,38);
s2 := Sym(38)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)
(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38);
s3 := Sym(38)!( 3, 4)( 6,10)( 7, 9)( 8,11)(12,13)(15,19)(16,18)(17,20)(21,31)
(22,30)(23,32)(24,37)(25,36)(26,38)(27,34)(28,33)(29,35);
s4 := Sym(38)!( 3,21)( 4,22)( 5,23)( 6,24)( 7,25)( 8,26)( 9,27)(10,28)(11,29)
(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38);
poly := sub<Sym(38)|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*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope