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# Polytope of Type {12,6}

Atlas Canonical Name : {12,6}*1728j
if this polytope has a name.
Group : SmallGroup(1728,47847)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 144, 432, 72
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 : {12,6}*432h
9-fold quotients : {12,6}*192a
12-fold quotients : {4,6}*144
18-fold quotients : {6,6}*96
24-fold quotients : {4,6}*72
36-fold quotients : {3,6}*48, {6,3}*48
72-fold quotients : {3,3}*24
108-fold quotients : {4,2}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,29)( 6,30)( 7,32)( 8,31)( 9,21)(10,22)(11,24)(12,23)(13,25)
(14,26)(15,28)(16,27)(19,20)(35,36);;
s1 := ( 2, 4)( 6, 8)(10,12)(13,33)(14,36)(15,35)(16,34)(17,25)(18,28)(19,27)
(20,26)(21,29)(22,32)(23,31)(24,30);;
s2 := ( 1,18)( 2,17)( 3,19)( 4,20)( 5,14)( 6,13)( 7,15)( 8,16)( 9,22)(10,21)
(11,23)(12,24)(25,30)(26,29)(27,31)(28,32)(33,34);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope