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# Polytope of Type {3,2,2,5,10}

Atlas Canonical Name : {3,2,2,5,10}*1200
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 6
Schlafli Type : {3,2,2,5,10}
Number of vertices, edges, etc : 3, 3, 2, 5, 25, 10
Order of s0s1s2s3s4s5 : 30
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) :
5-fold quotients : {3,2,2,5,2}*240
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,18)(19,24)(20,23)(21,26)(22,25)
(27,30)(28,29);;
s4 := ( 6,12)( 7, 9)( 8,19)(10,21)(11,15)(13,17)(14,23)(16,27)(18,22)(20,25)
(24,29)(26,28);;
s5 := ( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);;
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*s2*s0*s2, s1*s2*s1*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,
s0*s1*s0*s1*s0*s1, 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(30)!(2,3);
s1 := Sym(30)!(1,2);
s2 := Sym(30)!(4,5);
s3 := Sym(30)!( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,18)(19,24)(20,23)(21,26)
(22,25)(27,30)(28,29);
s4 := Sym(30)!( 6,12)( 7, 9)( 8,19)(10,21)(11,15)(13,17)(14,23)(16,27)(18,22)
(20,25)(24,29)(26,28);
s5 := Sym(30)!( 9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30);
poly := sub<Sym(30)|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*s2*s0*s2, s1*s2*s1*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, s0*s1*s0*s1*s0*s1, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope