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# Polytope of Type {2,12,12}

Atlas Canonical Name : {2,12,12}*1728m
if this polytope has a name.
Group : SmallGroup(1728,47870)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 36, 216, 36
Order of s0s1s2s3 : 12
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) :
12-fold quotients : {2,4,4}*144
36-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 7,15)( 8,17)( 9,16)(10,18)(11,27)(12,29)(13,28)(14,30)(20,21)
(23,31)(24,33)(25,32)(26,34)(36,37);;
s2 := ( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(16,18)(19,23)(20,26)(21,25)(22,24)
(28,30)(31,35)(32,38)(33,37)(34,36);;
s3 := ( 3,22)( 4,20)( 5,21)( 6,19)( 7,10)(11,34)(12,32)(13,33)(14,31)(15,18)
(23,30)(24,28)(25,29)(26,27)(35,38);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope