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# Polytope of Type {4,6}

Atlas Canonical Name : {4,6}*192b
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {4,6}
Number of vertices, edges, etc : 16, 48, 24
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Halving Operation
Facet Of :
{4,6,2} of size 384
{4,6,3} of size 768
{4,6,3} of size 768
{4,6,4} of size 768
{4,6,4} of size 768
{4,6,4} of size 768
{4,6,6} of size 1152
{4,6,6} of size 1152
{4,6,4} of size 1152
{4,6,10} of size 1920
{4,6,6} of size 1920
Vertex Figure Of :
{2,4,6} of size 384
{4,4,6} of size 768
{6,4,6} of size 1152
{10,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6}*96
4-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
8-fold quotients : {4,3}*24, {2,6}*24
12-fold quotients : {4,2}*16
16-fold quotients : {2,3}*12
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12}*384d, {8,6}*384f, {8,6}*384g, {4,12}*384e, {4,6}*384b
3-fold covers : {4,18}*576b, {12,6}*576b, {12,6}*576f
4-fold covers : {8,6}*768j, {8,12}*768o, {8,12}*768p, {4,6}*768a, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,6}*768k, {8,12}*768w, {4,12}*768f, {4,24}*768l, {8,6}*768l, {16,6}*768b, {16,6}*768c
5-fold covers : {20,6}*960e, {4,30}*960b
6-fold covers : {4,36}*1152d, {8,18}*1152f, {8,18}*1152g, {4,36}*1152e, {4,18}*1152b, {24,6}*1152d, {24,6}*1152h, {12,6}*1152d, {12,12}*1152i, {12,12}*1152n, {12,12}*1152o, {24,6}*1152k, {24,6}*1152l, {12,12}*1152r, {12,6}*1152f
7-fold covers : {28,6}*1344e, {4,42}*1344b
9-fold covers : {4,54}*1728b, {36,6}*1728b, {12,18}*1728c, {12,6}*1728b, {12,18}*1728d, {12,6}*1728f, {12,6}*1728i, {4,6}*1728
10-fold covers : {40,6}*1920b, {40,6}*1920d, {20,6}*1920b, {20,12}*1920b, {20,12}*1920c, {4,60}*1920d, {8,30}*1920f, {8,30}*1920g, {4,60}*1920e, {4,30}*1920b
Permutation Representation (GAP) :
```s0 := ( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 1, 3)( 2, 4)( 7, 9)( 8,10);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope