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# Polytope of Type {6,3,12}

Atlas Canonical Name : {6,3,12}*864
if this polytope has a name.
Group : SmallGroup(864,4673)
Rank : 4
Schlafli Type : {6,3,12}
Number of vertices, edges, etc : 6, 18, 36, 24
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,3,12,2} of size 1728
Vertex Figure Of :
{2,6,3,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {6,3,4}*288, {2,3,12}*288
4-fold quotients : {6,3,6}*216
6-fold quotients : {6,3,4}*144
9-fold quotients : {2,3,4}*96
12-fold quotients : {2,3,6}*72, {6,3,2}*72
18-fold quotients : {2,3,4}*48
36-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,3,24}*1728, {6,6,12}*1728d
Permutation Representation (GAP) :
```s0 := ( 5, 9)( 6,10)( 7,11)( 8,12)(17,21)(18,22)(19,23)(20,24)(29,33)(30,34)
(31,35)(32,36);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)(10,11)(13,29)(14,31)(15,30)(16,32)(17,25)
(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36);;
s2 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)
(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,28)(14,27)(15,26)(16,25)
(17,32)(18,31)(19,30)(20,29)(21,36)(22,35)(23,34)(24,33);;
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, s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope