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# Polytope of Type {10,6,3}

Atlas Canonical Name : {10,6,3}*1080
Also Known As : {{10,6|2},{6,3}6}. if this polytope has another name.
Group : SmallGroup(1080,287)
Rank : 4
Schlafli Type : {10,6,3}
Number of vertices, edges, etc : 10, 90, 27, 9
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
3-fold quotients : {10,6,3}*360
5-fold quotients : {2,6,3}*216
9-fold quotients : {10,2,3}*120
15-fold quotients : {2,6,3}*72
18-fold quotients : {5,2,3}*60
45-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(19,28)(20,29)(21,30)(22,25)
(23,26)(24,27)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42);;
s1 := ( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,19)(17,21)(18,20)
(22,28)(23,30)(24,29)(26,27)(31,34)(32,36)(33,35)(37,43)(38,45)(39,44)
(41,42);;
s2 := (16,33)(17,31)(18,32)(19,36)(20,34)(21,35)(22,39)(23,37)(24,38)(25,42)
(26,40)(27,41)(28,45)(29,43)(30,44);;
s3 := ( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,23)( 9,24)(10,25)
(11,26)(12,27)(13,28)(14,29)(15,30);;
poly := Group([s0,s1,s2,s3]);;

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

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

```
References : None.
to this polytope