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# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*1728j
if this polytope has a name.
Group : SmallGroup(1728,47847)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 72, 432, 144
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {6,12}*432h
9-fold quotients : {6,12}*192a
12-fold quotients : {6,4}*144
18-fold quotients : {6,6}*96
24-fold quotients : {6,4}*72
36-fold quotients : {3,6}*48, {6,3}*48
72-fold quotients : {3,3}*24
108-fold quotients : {2,4}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,25)(14,26)(15,28)(16,27)(17,33)
(18,34)(19,36)(20,35)(21,29)(22,30)(23,32)(24,31);;
s1 := ( 1,13)( 2,16)( 3,15)( 4,14)( 6, 8)( 9,33)(10,36)(11,35)(12,34)(17,29)
(18,32)(19,31)(20,30)(22,24)(26,28);;
s2 := ( 1, 2)( 5, 6)( 9,10)(13,34)(14,33)(15,35)(16,36)(17,26)(18,25)(19,27)
(20,28)(21,30)(22,29)(23,31)(24,32);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

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

```
References : None.
to this polytope