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# Polytope of Type {2,12,12}

Atlas Canonical Name : {2,12,12}*1728o
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
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) :
4-fold quotients : {2,6,12}*432c
9-fold quotients : {2,4,12}*192c
12-fold quotients : {2,6,4}*144
18-fold quotients : {2,4,6}*96c
36-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)(18,28)
(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,19)(16,21)(17,20)(18,22)(24,25)
(27,31)(28,33)(29,32)(30,34)(36,37);;
s3 := ( 4, 6)( 7,15)( 8,18)( 9,17)(10,16)(11,27)(12,30)(13,29)(14,28)(20,22)
(23,31)(24,34)(25,33)(26,32)(36,38);;
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*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope