# Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*576l
if this polytope has a name.
Group : SmallGroup(576,8653)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 24, 144, 24
Order of s0s1s2 : 3
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,12,2} of size 1152
Vertex Figure Of :
{2,12,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {6,12}*144d, {12,6}*144d
12-fold quotients : {4,6}*48b, {6,4}*48b
24-fold quotients : {3,4}*24, {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,24}*1152y, {12,24}*1152z, {24,12}*1152y, {24,12}*1152z, {12,12}*1152t
3-fold covers : {12,36}*1728i, {36,12}*1728i, {12,12}*1728u
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);;
s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);;
s2 := ( 1, 4)( 2, 3)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11);;
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*s0*s1*s2*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(16)!( 1, 9)( 2,11)( 3,10)( 4,12)( 5,13)( 6,15)( 7,14)( 8,16);
s1 := Sym(16)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16);
s2 := Sym(16)!( 1, 4)( 2, 3)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11);
poly := sub<Sym(16)|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*s0*s1*s2*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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 >;

```
References : None.
to this polytope