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# Polytope of Type {8,2,10,5}

Atlas Canonical Name : {8,2,10,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,8167)
Rank : 5
Schlafli Type : {8,2,10,5}
Number of vertices, edges, etc : 8, 8, 10, 25, 5
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,10,5}*800
4-fold quotients : {2,2,10,5}*400
5-fold quotients : {8,2,2,5}*320
10-fold quotients : {4,2,2,5}*160
20-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33);;
s3 := ( 9,12)(10,18)(11,15)(13,20)(14,26)(16,28)(17,22)(19,24)(23,32)(25,29)
(27,30)(31,33);;
s4 := ( 9,10)(11,14)(12,16)(13,15)(18,23)(19,22)(20,25)(21,24)(26,27)(28,31)
(29,30)(32,33);;
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,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(33)!(2,3)(4,5)(6,7);
s1 := Sym(33)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(33)!(12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)
(32,33);
s3 := Sym(33)!( 9,12)(10,18)(11,15)(13,20)(14,26)(16,28)(17,22)(19,24)(23,32)
(25,29)(27,30)(31,33);
s4 := Sym(33)!( 9,10)(11,14)(12,16)(13,15)(18,23)(19,22)(20,25)(21,24)(26,27)
(28,31)(29,30)(32,33);
poly := sub<Sym(33)|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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope