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

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

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

```

to this polytope