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

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

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

```

to this polytope