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# Polytope of Type {2,6,8,2}

Atlas Canonical Name : {2,6,8,2}*384
if this polytope has a name.
Group : SmallGroup(384,19745)
Rank : 5
Schlafli Type : {2,6,8,2}
Number of vertices, edges, etc : 2, 6, 24, 8, 2
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,8,2,2} of size 768
{2,6,8,2,3} of size 1152
{2,6,8,2,5} of size 1920
Vertex Figure Of :
{2,2,6,8,2} of size 768
{3,2,6,8,2} of size 1152
{5,2,6,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,4,2}*192a
3-fold quotients : {2,2,8,2}*128
4-fold quotients : {2,6,2,2}*96
6-fold quotients : {2,2,4,2}*64
8-fold quotients : {2,3,2,2}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,8,4}*768a, {2,12,8,2}*768a, {4,6,8,2}*768a, {2,6,16,2}*768
3-fold covers : {2,18,8,2}*1152, {2,6,8,6}*1152, {6,6,8,2}*1152a, {6,6,8,2}*1152b, {2,6,24,2}*1152a, {2,6,24,2}*1152b
5-fold covers : {2,30,8,2}*1920, {2,6,8,10}*1920, {10,6,8,2}*1920, {2,6,40,2}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(25,26);;
s2 := ( 3, 5)( 4,11)( 7, 8)( 9,12)(10,17)(13,14)(15,18)(16,23)(19,20)(21,24)
(22,25);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,22)
(23,25)(24,26);;
s4 := (27,28);;
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,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*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*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope