# Polytope of Type {12,12}

Atlas Canonical Name : {12,12}*864m
if this polytope has a name.
Group : SmallGroup(864,4669)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 36, 216, 36
Order of s0s1s2 : 12
Order of s0s1s2s1 : 3
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,12,2} of size 1728
Vertex Figure Of :
{2,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
12-fold quotients : {4,4}*72
36-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12}*1728z
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5,13)( 6,15)( 7,14)( 8,16)( 9,25)(10,27)(11,26)(12,28)(18,19)
(21,29)(22,31)(23,30)(24,32)(34,35);;
s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)
(26,28)(29,33)(30,36)(31,35)(32,34);;
s2 := ( 1,20)( 2,18)( 3,19)( 4,17)( 5, 8)( 9,32)(10,30)(11,31)(12,29)(13,16)
(21,28)(22,26)(23,27)(24,25)(33,36);;
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope