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

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

```
Permutation Representation (Magma) :
```s0 := Sym(16)!(2,3)(4,5)(6,7);
s1 := Sym(16)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(16)!(11,12)(13,14);
s3 := Sym(16)!( 9,13)(10,11)(12,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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, s1*s2*s1*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope