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# Polytope of Type {2,10,4,2,5}

Atlas Canonical Name : {2,10,4,2,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,10169)
Rank : 6
Schlafli Type : {2,10,4,2,5}
Number of vertices, edges, etc : 2, 10, 20, 4, 5, 5
Order of s0s1s2s3s4s5 : 20
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,10,2,2,5}*800
4-fold quotients : {2,5,2,2,5}*400
5-fold quotients : {2,2,4,2,5}*320
10-fold quotients : {2,2,2,2,5}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);;
s2 := ( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);;
s3 := ( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)(20,22);;
s4 := (24,25)(26,27);;
s5 := (23,24)(25,26);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 5, 6)( 8, 9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);
s2 := Sym(27)!( 3, 5)( 4,13)( 6,10)( 7, 8)( 9,19)(12,17)(14,15)(16,20)(18,21);
s3 := Sym(27)!( 3, 4)( 5, 8)( 6, 9)( 7,12)(10,15)(11,16)(13,17)(14,18)(19,21)
(20,22);
s4 := Sym(27)!(24,25)(26,27);
s5 := Sym(27)!(23,24)(25,26);
poly := sub<Sym(27)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope