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# Polytope of Type {12,4}

Atlas Canonical Name : {12,4}*288
if this polytope has a name.
Group : SmallGroup(288,889)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 36, 72, 12
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{12,4,2} of size 576
{12,4,4} of size 1152
{12,4,6} of size 1728
Vertex Figure Of :
{2,12,4} of size 576
{4,12,4} of size 1152
{6,12,4} of size 1728
{6,12,4} of size 1728
{3,12,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4}*144
4-fold quotients : {6,4}*72
9-fold quotients : {4,4}*32
18-fold quotients : {2,4}*16, {4,2}*16
36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4}*576, {12,8}*576a, {24,4}*576a, {24,4}*576b, {12,8}*576b
3-fold covers : {12,4}*864b, {12,12}*864f, {12,12}*864g, {12,4}*864d, {12,12}*864j, {12,12}*864l
4-fold covers : {24,4}*1152a, {12,8}*1152a, {24,8}*1152a, {24,8}*1152b, {24,8}*1152c, {24,8}*1152d, {48,4}*1152a, {12,16}*1152a, {48,4}*1152b, {12,16}*1152b, {12,4}*1152a, {12,8}*1152b, {24,4}*1152b
5-fold covers : {60,4}*1440, {12,20}*1440
6-fold covers : {12,4}*1728b, {12,12}*1728f, {12,12}*1728g, {12,8}*1728a, {12,24}*1728g, {12,24}*1728h, {24,4}*1728a, {24,12}*1728i, {24,12}*1728j, {24,4}*1728c, {24,12}*1728k, {24,12}*1728l, {12,8}*1728d, {12,24}*1728m, {12,24}*1728n, {24,4}*1728f, {24,12}*1728q, {24,4}*1728g, {24,12}*1728r, {12,8}*1728g, {12,24}*1728s, {12,8}*1728h, {12,24}*1728t, {12,4}*1728c, {12,12}*1728q, {12,12}*1728t, {12,24}*1728u, {24,12}*1728v, {24,12}*1728w, {12,24}*1728x
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11);;
s1 := ( 1, 8)( 2, 7)( 3, 9)( 4,11)( 5,10)( 6,12);;
s2 := ( 8, 9)(11,12);;
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,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope