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# Polytope of Type {3,2,8,2}

Atlas Canonical Name : {3,2,8,2}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 5
Schlafli Type : {3,2,8,2}
Number of vertices, edges, etc : 3, 3, 8, 8, 2
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,8,2,2} of size 384
{3,2,8,2,3} of size 576
{3,2,8,2,4} of size 768
{3,2,8,2,5} of size 960
{3,2,8,2,6} of size 1152
{3,2,8,2,7} of size 1344
{3,2,8,2,9} of size 1728
{3,2,8,2,10} of size 1920
Vertex Figure Of :
{2,3,2,8,2} of size 384
{3,3,2,8,2} of size 768
{4,3,2,8,2} of size 768
{6,3,2,8,2} of size 1152
{5,3,2,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,4,2}*96
4-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,8,4}*384a, {3,2,16,2}*384, {6,2,8,2}*384
3-fold covers : {9,2,8,2}*576, {3,2,24,2}*576, {3,2,8,6}*576, {3,6,8,2}*576
4-fold covers : {3,2,8,4}*768a, {3,2,8,8}*768b, {3,2,8,8}*768c, {3,2,16,4}*768a, {3,2,16,4}*768b, {3,2,32,2}*768, {6,2,8,4}*768a, {6,4,8,2}*768a, {12,2,8,2}*768, {6,2,16,2}*768, {3,4,8,2}*768
5-fold covers : {3,2,40,2}*960, {3,2,8,10}*960, {15,2,8,2}*960
6-fold covers : {9,2,8,4}*1152a, {3,2,8,12}*1152a, {3,6,8,4}*1152a, {3,2,24,4}*1152a, {9,2,16,2}*1152, {3,2,16,6}*1152, {3,6,16,2}*1152, {3,2,48,2}*1152, {18,2,8,2}*1152, {6,2,8,6}*1152, {6,6,8,2}*1152a, {6,6,8,2}*1152c, {6,2,24,2}*1152
7-fold covers : {3,2,56,2}*1344, {3,2,8,14}*1344, {21,2,8,2}*1344
9-fold covers : {27,2,8,2}*1728, {3,2,72,2}*1728, {9,2,24,2}*1728, {3,6,24,2}*1728a, {3,2,8,18}*1728, {9,2,8,6}*1728, {9,6,8,2}*1728, {3,6,8,2}*1728a, {3,2,24,6}*1728a, {3,2,24,6}*1728b, {3,6,24,2}*1728b, {3,6,8,6}*1728, {3,2,24,6}*1728c, {3,2,8,6}*1728, {3,6,8,2}*1728b
10-fold covers : {15,2,8,4}*1920a, {3,2,8,20}*1920a, {3,2,40,4}*1920a, {15,2,16,2}*1920, {3,2,16,10}*1920, {3,2,80,2}*1920, {30,2,8,2}*1920, {6,2,8,10}*1920, {6,10,8,2}*1920, {6,2,40,2}*1920
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s4 := (12,13);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2);
s2 := Sym(13)!( 5, 6)( 7, 8)( 9,10);
s3 := Sym(13)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s4 := Sym(13)!(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope