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# Polytope of Type {3,24,2}

Atlas Canonical Name : {3,24,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {3,24,2}
Number of vertices, edges, etc : 12, 144, 96, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 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) :
3-fold quotients : {3,8,2}*384
4-fold quotients : {3,12,2}*288
12-fold quotients : {3,4,2}*96
16-fold quotients : {3,6,2}*72
24-fold quotients : {3,4,2}*48
48-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)
(32,48);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)
(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)(43,47)
(44,45);;
s2 := ( 1,15)( 2,16)( 3,13)( 4,14)( 5,11)( 6,12)( 7, 9)( 8,10)(17,47)(18,48)
(19,45)(20,46)(21,43)(22,44)(23,41)(24,42)(25,39)(26,40)(27,37)(28,38)(29,35)
(30,36)(31,33)(32,34);;
s3 := (49,50);;
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,
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(50)!( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)
(20,35)(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)
(31,47)(32,48);
s1 := Sym(50)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)
(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)
(43,47)(44,45);
s2 := Sym(50)!( 1,15)( 2,16)( 3,13)( 4,14)( 5,11)( 6,12)( 7, 9)( 8,10)(17,47)
(18,48)(19,45)(20,46)(21,43)(22,44)(23,41)(24,42)(25,39)(26,40)(27,37)(28,38)
(29,35)(30,36)(31,33)(32,34);
s3 := Sym(50)!(49,50);
poly := sub<Sym(50)|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, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

```

to this polytope