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

Atlas Canonical Name : {2,4,2,5,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,10169)
Rank : 6
Schlafli Type : {2,4,2,5,10}
Number of vertices, edges, etc : 2, 4, 4, 5, 25, 10
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 : {2,2,2,5,10}*800
5-fold quotients : {2,4,2,5,2}*320
10-fold quotients : {2,2,2,5,2}*160
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,24)(22,27)(23,26)
(28,31)(29,30);;
s4 := ( 7,13)( 8,10)( 9,20)(11,22)(12,16)(14,18)(15,24)(17,28)(19,23)(21,26)
(25,30)(27,29);;
s5 := (10,11)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31);;
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, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s1*s2*s1*s2*s1*s2, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(31)!(1,2);
s1 := Sym(31)!(4,5);
s2 := Sym(31)!(3,4)(5,6);
s3 := Sym(31)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,24)(22,27)
(23,26)(28,31)(29,30);
s4 := Sym(31)!( 7,13)( 8,10)( 9,20)(11,22)(12,16)(14,18)(15,24)(17,28)(19,23)
(21,26)(25,30)(27,29);
s5 := Sym(31)!(10,11)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)
(30,31);
poly := sub<Sym(31)|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, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope