# Polytope of Type {4,4,6}

Atlas Canonical Name : {4,4,6}*384a
Also Known As : {{4,4}4,{4,6|2}}. if this polytope has another name.
Group : SmallGroup(384,12882)
Rank : 4
Schlafli Type : {4,4,6}
Number of vertices, edges, etc : 8, 16, 24, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,4,6,2} of size 768
{4,4,6,3} of size 1152
Vertex Figure Of :
{2,4,4,6} of size 768
{3,4,4,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,6}*192
3-fold quotients : {4,4,2}*128
4-fold quotients : {2,4,6}*96a, {4,2,6}*96
6-fold quotients : {4,4,2}*64
8-fold quotients : {4,2,3}*48, {2,2,6}*48
12-fold quotients : {2,4,2}*32, {4,2,2}*32
16-fold quotients : {2,2,3}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8,6}*768a, {8,4,6}*768a, {4,4,12}*768a, {4,4,6}*768a, {4,8,6}*768b, {8,4,6}*768b
3-fold covers : {4,4,18}*1152a, {4,12,6}*1152b, {12,4,6}*1152a, {4,12,6}*1152c
5-fold covers : {4,4,30}*1920a, {4,20,6}*1920a, {20,4,6}*1920a
Permutation Representation (GAP) :
```s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)
(11,23)(12,24);;
s1 := (19,22)(20,23)(21,24);;
s2 := ( 1, 7)( 2, 9)( 3, 8)( 4,10)( 5,12)( 6,11)(13,19)(14,21)(15,20)(16,22)
(17,24)(18,23);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(24)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)
(10,22)(11,23)(12,24);
s1 := Sym(24)!(19,22)(20,23)(21,24);
s2 := Sym(24)!( 1, 7)( 2, 9)( 3, 8)( 4,10)( 5,12)( 6,11)(13,19)(14,21)(15,20)
(16,22)(17,24)(18,23);
s3 := Sym(24)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23);
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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```
References : None.
to this polytope