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# Polytope of Type {2,2,4,8}

Atlas Canonical Name : {2,2,4,8}*256b
if this polytope has a name.
Group : SmallGroup(256,53366)
Rank : 5
Schlafli Type : {2,2,4,8}
Number of vertices, edges, etc : 2, 2, 4, 16, 8
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,4,8,2} of size 512
Vertex Figure Of :
{2,2,2,4,8} of size 512
{3,2,2,4,8} of size 768
{5,2,2,4,8} of size 1280
{7,2,2,4,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,4,4}*128
4-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,4,8}*512a, {2,2,8,8}*512c, {2,2,8,8}*512d, {2,4,4,8}*512a
3-fold covers : {2,6,4,8}*768b, {6,2,4,8}*768b, {2,2,12,8}*768b, {2,2,4,24}*768b
5-fold covers : {2,10,4,8}*1280b, {10,2,4,8}*1280b, {2,2,20,8}*1280b, {2,2,4,40}*1280b
7-fold covers : {2,14,4,8}*1792b, {14,2,4,8}*1792b, {2,2,28,8}*1792b, {2,2,4,56}*1792b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 8)( 7,10)( 9,12)(13,16)(15,19)(17,18);;
s3 := ( 5, 6)( 7, 9)( 8,11)(10,13)(12,15)(14,17)(16,19)(18,20);;
s4 := ( 6, 7)( 8,10)( 9,12)(11,14)(15,18)(17,19);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;

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

```

to this polytope