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# Polytope of Type {9,2,3,12}

Atlas Canonical Name : {9,2,3,12}*1728
if this polytope has a name.
Group : SmallGroup(1728,30201)
Rank : 5
Schlafli Type : {9,2,3,12}
Number of vertices, edges, etc : 9, 9, 4, 24, 16
Order of s0s1s2s3s4 : 72
Order of s0s1s2s3s4s3s2s1 : 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 : {9,2,3,6}*864
3-fold quotients : {3,2,3,12}*576
4-fold quotients : {9,2,3,3}*432
6-fold quotients : {3,2,3,6}*288
12-fold quotients : {3,2,3,3}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)(25,47)
(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)(45,57)
(48,49);;
s3 := (10,13)(11,22)(12,18)(15,51)(16,50)(17,34)(19,23)(20,56)(21,57)(24,49)
(25,48)(26,33)(27,30)(28,29)(31,32)(36,53)(37,55)(38,42)(39,45)(40,41)(43,44)
(46,47);;
s4 := (10,53)(11,48)(12,49)(13,42)(14,56)(15,21)(16,20)(17,55)(18,30)(19,50)
(22,33)(23,51)(24,39)(25,38)(26,37)(27,36)(28,43)(29,52)(31,40)(32,54)(34,45)
(35,57)(41,47)(44,46);;
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, s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3,
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(57)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(57)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(57)!(11,12)(13,14)(15,28)(16,31)(18,23)(19,22)(20,40)(21,43)(24,46)
(25,47)(26,32)(27,29)(30,51)(33,50)(34,35)(36,52)(37,54)(38,41)(39,44)(42,56)
(45,57)(48,49);
s3 := Sym(57)!(10,13)(11,22)(12,18)(15,51)(16,50)(17,34)(19,23)(20,56)(21,57)
(24,49)(25,48)(26,33)(27,30)(28,29)(31,32)(36,53)(37,55)(38,42)(39,45)(40,41)
(43,44)(46,47);
s4 := Sym(57)!(10,53)(11,48)(12,49)(13,42)(14,56)(15,21)(16,20)(17,55)(18,30)
(19,50)(22,33)(23,51)(24,39)(25,38)(26,37)(27,36)(28,43)(29,52)(31,40)(32,54)
(34,45)(35,57)(41,47)(44,46);
poly := sub<Sym(57)|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,
s4*s2*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope