Questions?
See the FAQ
or other info.

# Polytope of Type {12,4}

Atlas Canonical Name : {12,4}*216
if this polytope has a name.
Group : SmallGroup(216,87)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 27, 54, 9
Order of s0s1s2 : 6
Order of s0s1s2s1 : 3
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{12,4,2} of size 432
Vertex Figure Of :
{2,12,4} of size 432
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,4}*72
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4}*432a
3-fold covers : {12,12}*648
4-fold covers : {12,4}*864a
6-fold covers : {12,4}*1296, {12,12}*1296a, {12,12}*1296e
8-fold covers : {12,4}*1728a, {12,8}*1728b, {24,4}*1728b, {12,8}*1728c, {24,4}*1728d
9-fold covers : {12,4}*1944a, {12,4}*1944b, {12,4}*1944c, {12,4}*1944d
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(11,12)(13,14)(16,18);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(18)!( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);
s2 := Sym(18)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(11,12)(13,14)(16,18);
poly := sub<Sym(18)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope