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

Atlas Canonical Name : {8,2,5,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,8167)
Rank : 5
Schlafli Type : {8,2,5,10}
Number of vertices, edges, etc : 8, 8, 5, 25, 10
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 : {4,2,5,10}*800
4-fold quotients : {2,2,5,10}*400
5-fold quotients : {8,2,5,2}*320
10-fold quotients : {4,2,5,2}*160
20-fold quotients : {2,2,5,2}*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 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,26)(24,29)(25,28)
(30,33)(31,32);;
s3 := ( 9,15)(10,12)(11,22)(13,24)(14,18)(16,20)(17,26)(19,30)(21,25)(23,28)
(27,32)(29,31);;
s4 := (12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(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*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,26)(24,29)
(25,28)(30,33)(31,32);
s3 := Sym(33)!( 9,15)(10,12)(11,22)(13,24)(14,18)(16,20)(17,26)(19,30)(21,25)
(23,28)(27,32)(29,31);
s4 := Sym(33)!(12,13)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)
(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*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope