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# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*192a
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 8, 48, 16
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{6,12,2} of size 384
{6,12,4} of size 768
{6,12,6} of size 1152
{6,12,6} of size 1152
{6,12,6} of size 1728
{6,12,10} of size 1920
{6,12,6} of size 1920
Vertex Figure Of :
{2,6,12} of size 384
{4,6,12} of size 768
{3,6,12} of size 960
{6,6,12} of size 1152
{10,6,12} of size 1920
{6,6,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6}*96
4-fold quotients : {3,6}*48, {6,3}*48
8-fold quotients : {3,3}*24
12-fold quotients : {2,4}*16
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12}*384a, {6,12}*384, {12,12}*384c, {6,24}*384a, {6,24}*384b
3-fold covers : {6,12}*576a, {6,12}*576e
4-fold covers : {6,24}*768, {12,24}*768a, {12,24}*768b, {6,12}*768f, {12,12}*768a, {12,12}*768b, {12,12}*768c, {12,24}*768c, {24,12}*768c, {12,24}*768d, {24,12}*768d, {6,12}*768g, {12,24}*768e, {24,12}*768e, {12,24}*768f, {24,12}*768f, {6,12}*768h, {6,48}*768a, {6,48}*768b
5-fold covers : {6,60}*960a, {30,12}*960b
6-fold covers : {12,12}*1152f, {6,12}*1152a, {6,24}*1152g, {6,24}*1152i, {12,12}*1152j, {12,12}*1152l, {6,24}*1152j, {6,12}*1152e, {12,12}*1152q, {6,24}*1152m
7-fold covers : {6,84}*1344a, {42,12}*1344b
9-fold covers : {6,36}*1728a, {18,12}*1728b, {6,12}*1728a, {6,12}*1728e, {6,12}*1728h, {6,12}*1728j
10-fold covers : {12,60}*1920b, {6,60}*1920, {6,120}*1920a, {6,120}*1920b, {12,60}*1920c, {60,12}*1920c, {30,24}*1920a, {30,12}*1920, {60,12}*1920d, {30,24}*1920b
Permutation Representation (GAP) :
```s0 := ( 1, 5)( 2, 6)( 7,11)( 8,12);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,12)(10,11);;
s2 := ( 1,11)( 2,12)( 3,10)( 4, 9)( 5, 7)( 6, 8);;
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, 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope