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# Polytope of Type {8,6}

Atlas Canonical Name : {8,6}*192c
if this polytope has a name.
Group : SmallGroup(192,1485)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 16, 48, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{8,6,2} of size 384
{8,6,4} of size 768
{8,6,4} of size 768
{8,6,4} of size 768
{8,6,6} of size 1152
{8,6,6} of size 1152
{8,6,10} of size 1920
Vertex Figure Of :
{2,8,6} of size 384
{4,8,6} of size 768
{6,8,6} of size 1152
{10,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6}*96
4-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
8-fold quotients : {4,3}*24, {2,6}*24
16-fold quotients : {2,3}*12
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,12}*384f, {8,6}*384f, {8,12}*384g
3-fold covers : {8,18}*576c, {24,6}*576c, {24,6}*576d
4-fold covers : {8,6}*768g, {8,6}*768h, {8,6}*768i, {8,24}*768k, {8,24}*768l, {8,6}*768j, {8,24}*768m, {8,12}*768p, {8,24}*768o, {8,12}*768s
5-fold covers : {40,6}*960d, {8,30}*960c
6-fold covers : {8,36}*1152f, {8,18}*1152f, {8,36}*1152g, {24,12}*1152i, {24,12}*1152j, {24,6}*1152d, {24,12}*1152n, {24,6}*1152l, {24,12}*1152u
7-fold covers : {56,6}*1344b, {8,42}*1344c
9-fold covers : {8,54}*1728c, {72,6}*1728b, {24,18}*1728c, {24,18}*1728d, {24,6}*1728c, {24,6}*1728d, {24,6}*1728g
10-fold covers : {40,12}*1920e, {40,6}*1920b, {40,12}*1920g, {8,60}*1920f, {8,30}*1920f, {8,60}*1920g
Permutation Representation (GAP) :
```s0 := ( 1,11)( 2,12)( 3,10)( 4, 9)( 5,15)( 6,16)( 7,14)( 8,13);;
s1 := ( 3, 5)( 4, 6)( 7, 8)(11,13)(12,14)(15,16);;
s2 := ( 3, 4)( 5, 7)( 6, 8)( 9,10)(13,16)(14,15);;
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*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope