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# Polytope of Type {2,6,8}

Atlas Canonical Name : {2,6,8}*384c
if this polytope has a name.
Group : SmallGroup(384,20070)
Rank : 4
Schlafli Type : {2,6,8}
Number of vertices, edges, etc : 2, 12, 48, 16
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,8,2} of size 768
Vertex Figure Of :
{2,2,6,8} of size 768
{3,2,6,8} of size 1152
{5,2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,4}*192
4-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
8-fold quotients : {2,3,4}*48, {2,6,2}*48
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,8}*768f, {2,6,8}*768f, {2,12,8}*768g, {4,6,8}*768b
3-fold covers : {2,18,8}*1152c, {2,6,24}*1152c, {2,6,24}*1152d, {6,6,8}*1152d, {6,6,8}*1152e
5-fold covers : {2,6,40}*1920b, {10,6,8}*1920b, {2,30,8}*1920c
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 7)( 6, 8)( 9,10)(11,12)(13,16)(14,15);;
s2 := ( 5, 6)( 7, 9)( 8,10)(13,14)(15,17)(16,18);;
s3 := ( 3,17)( 4,18)( 5,15)( 6,16)( 7,14)( 8,13)( 9,12)(10,11);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 5, 7)( 6, 8)( 9,10)(11,12)(13,16)(14,15);
s2 := Sym(18)!( 5, 6)( 7, 9)( 8,10)(13,14)(15,17)(16,18);
s3 := Sym(18)!( 3,17)( 4,18)( 5,15)( 6,16)( 7,14)( 8,13)( 9,12)(10,11);
poly := sub<Sym(18)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 >;

```

to this polytope