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# Polytope of Type {8,3}

Atlas Canonical Name : {8,3}*192
Also Known As : {8,3}6if this polytope has another name.
Group : SmallGroup(192,956)
Rank : 3
Schlafli Type : {8,3}
Number of vertices, edges, etc : 32, 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 :
{8,3,2} of size 384
{8,3,3} of size 768
{8,3,4} of size 768
{8,3,6} of size 1152
Vertex Figure Of :
{2,8,3} of size 384
{4,8,3} of size 768
{4,8,3} of size 768
{6,8,3} of size 1152
{10,8,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {4,3}*48
8-fold quotients : {4,3}*24
16-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,3}*384, {8,6}*384a, {8,6}*384e
3-fold covers : {8,9}*576, {24,3}*576
4-fold covers : {16,3}*768a, {16,3}*768b, {8,6}*768d, {8,12}*768l, {8,6}*768h, {8,12}*768n, {8,12}*768q, {8,6}*768k, {8,12}*768x
5-fold covers : {8,15}*960a
6-fold covers : {8,9}*1152, {8,18}*1152a, {8,18}*1152d, {24,3}*1152a, {24,6}*1152a, {24,6}*1152c, {24,6}*1152e
7-fold covers : {8,21}*1344
9-fold covers : {8,27}*1728, {24,9}*1728, {24,3}*1728
10-fold covers : {8,15}*1920a, {8,30}*1920a, {40,6}*1920c, {8,30}*1920d
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12);;
s1 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)(11,12);;
s2 := ( 3, 4)( 5, 9)( 6,10)( 7,11)( 8,12);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope