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

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

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

```

to this polytope