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Polytope of Type {12,6}

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

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

```
References : None.
to this polytope