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# Polytope of Type {3,8}

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

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

```
References : None.
to this polytope