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# Polytope of Type {8,4}

Atlas Canonical Name : {8,4}*256b
Also Known As : {8,4}4if this polytope has another name.
Group : SmallGroup(256,6661)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 32, 64, 16
Order of s0s1s2 : 4
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{8,4,2} of size 512
Vertex Figure Of :
{2,8,4} of size 512
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,4}*128b
4-fold quotients : {4,4}*64
8-fold quotients : {4,4}*32
16-fold quotients : {2,4}*16, {4,2}*16
32-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,4}*512c, {8,8}*512i, {8,8}*512p, {16,4}*512e, {16,4}*512f
3-fold covers : {24,4}*768b, {8,12}*768b
5-fold covers : {40,4}*1280b, {8,20}*1280b
7-fold covers : {56,4}*1792b, {8,28}*1792b
Permutation Representation (GAP) :
```s0 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 9)( 6,10)( 7,12)( 8,11);;
s1 := ( 5, 7)( 6, 8)(11,12)(13,14)(15,16);;
s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, 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 >;

```
References : None.
to this polytope