# Polytope of Type {12,3,6}

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

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

```
References : None.
to this polytope