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# Polytope of Type {8,4,2}

Atlas Canonical Name : {8,4,2}*256b
if this polytope has a name.
Group : SmallGroup(256,26531)
Rank : 4
Schlafli Type : {8,4,2}
Number of vertices, edges, etc : 16, 32, 8, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,4,2,2} of size 512
{8,4,2,3} of size 768
{8,4,2,5} of size 1280
{8,4,2,7} of size 1792
Vertex Figure Of :
{2,8,4,2} of size 512
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,2}*128
4-fold quotients : {4,4,2}*64
8-fold quotients : {2,4,2}*32, {4,2,2}*32
16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,4,2}*512a, {8,8,2}*512b, {8,8,2}*512c, {8,4,4}*512d, {8,4,2}*512b, {8,4,2}*512d, {8,8,2}*512f, {8,8,2}*512h
3-fold covers : {8,4,6}*768b, {24,4,2}*768b, {8,12,2}*768b
5-fold covers : {8,4,10}*1280b, {40,4,2}*1280b, {8,20,2}*1280b
7-fold covers : {8,4,14}*1792b, {56,4,2}*1792b, {8,28,2}*1792b
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);;
s1 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);;
s2 := ( 5, 7)( 6, 8)(13,15)(14,16);;
s3 := (17,18);;
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, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope