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# Polytope of Type {10,2,4,9}

Atlas Canonical Name : {10,2,4,9}*1440
if this polytope has a name.
Group : SmallGroup(1440,4569)
Rank : 5
Schlafli Type : {10,2,4,9}
Number of vertices, edges, etc : 10, 10, 4, 18, 9
Order of s0s1s2s3s4 : 90
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {5,2,4,9}*720
3-fold quotients : {10,2,4,3}*480
5-fold quotients : {2,2,4,9}*288
6-fold quotients : {5,2,4,3}*240
15-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,17)(13,19)(14,21)(15,23)(18,28)(20,30)(24,34)(31,40)(33,42)(35,43)
(37,44)(39,45);;
s3 := (11,12)(13,16)(14,15)(17,25)(18,24)(19,26)(20,22)(21,23)(27,33)(28,34)
(29,31)(30,32)(35,41)(36,42)(37,39)(38,40)(43,46)(44,45);;
s4 := (11,16)(12,14)(13,24)(15,20)(17,21)(18,33)(19,34)(22,29)(23,30)(25,26)
(27,41)(28,42)(31,37)(32,38)(35,39)(36,46)(40,44)(43,45);;
poly := Group([s0,s1,s2,s3,s4]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(46)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(46)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(46)!(12,17)(13,19)(14,21)(15,23)(18,28)(20,30)(24,34)(31,40)(33,42)
(35,43)(37,44)(39,45);
s3 := Sym(46)!(11,12)(13,16)(14,15)(17,25)(18,24)(19,26)(20,22)(21,23)(27,33)
(28,34)(29,31)(30,32)(35,41)(36,42)(37,39)(38,40)(43,46)(44,45);
s4 := Sym(46)!(11,16)(12,14)(13,24)(15,20)(17,21)(18,33)(19,34)(22,29)(23,30)
(25,26)(27,41)(28,42)(31,37)(32,38)(35,39)(36,46)(40,44)(43,45);
poly := sub<Sym(46)|s0,s1,s2,s3,s4>;

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

```

to this polytope