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

Atlas Canonical Name : {2,4,4,6}*384
if this polytope has a name.
Group : SmallGroup(384,18491)
Rank : 5
Schlafli Type : {2,4,4,6}
Number of vertices, edges, etc : 2, 4, 8, 12, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,4,6,2} of size 768
{2,4,4,6,3} of size 1152
Vertex Figure Of :
{2,2,4,4,6} of size 768
{3,2,4,4,6} of size 1152
{5,2,4,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
3-fold quotients : {2,4,4,2}*128
4-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
6-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
8-fold quotients : {2,2,2,3}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,4,6}*768, {2,4,4,12}*768, {2,4,8,6}*768a, {2,8,4,6}*768a, {2,4,8,6}*768b, {2,8,4,6}*768b, {2,4,4,6}*768a
3-fold covers : {2,4,4,18}*1152, {6,4,4,6}*1152, {2,4,12,6}*1152a, {2,12,4,6}*1152, {2,4,12,6}*1152c
5-fold covers : {2,4,4,30}*1920, {10,4,4,6}*1920, {2,4,20,6}*1920, {2,20,4,6}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)
(13,25)(14,26)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)
(36,48)(37,49)(38,50);;
s2 := (15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,30)(28,31)(29,32)(33,36)
(34,37)(35,38)(39,48)(40,49)(41,50)(42,45)(43,46)(44,47);;
s3 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)
(13,38)(14,37)(15,39)(16,41)(17,40)(18,42)(19,44)(20,43)(21,45)(22,47)(23,46)
(24,48)(25,50)(26,49);;
s4 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)
(12,24)(13,25)(14,26)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)
(35,47)(36,48)(37,49)(38,50);
s2 := Sym(50)!(15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,30)(28,31)(29,32)
(33,36)(34,37)(35,38)(39,48)(40,49)(41,50)(42,45)(43,46)(44,47);
s3 := Sym(50)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)
(12,36)(13,38)(14,37)(15,39)(16,41)(17,40)(18,42)(19,44)(20,43)(21,45)(22,47)
(23,46)(24,48)(25,50)(26,49);
s4 := Sym(50)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49);
poly := sub<Sym(50)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope