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# Polytope of Type {8,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,6}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 4
Schlafli Type : {8,2,6}
Number of vertices, edges, etc : 8, 8, 6, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,2,6,2} of size 384
{8,2,6,3} of size 576
{8,2,6,4} of size 768
{8,2,6,3} of size 768
{8,2,6,4} of size 768
{8,2,6,4} of size 768
{8,2,6,4} of size 1152
{8,2,6,6} of size 1152
{8,2,6,6} of size 1152
{8,2,6,6} of size 1152
{8,2,6,9} of size 1728
{8,2,6,3} of size 1728
{8,2,6,6} of size 1728
{8,2,6,10} of size 1920
{8,2,6,4} of size 1920
{8,2,6,5} of size 1920
{8,2,6,6} of size 1920
{8,2,6,5} of size 1920
{8,2,6,5} of size 1920
Vertex Figure Of :
{2,8,2,6} of size 384
{4,8,2,6} of size 768
{4,8,2,6} of size 768
{6,8,2,6} of size 1152
{3,8,2,6} of size 1152
{10,8,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,2,3}*96, {4,2,6}*96
3-fold quotients : {8,2,2}*64
4-fold quotients : {4,2,3}*48, {2,2,6}*48
6-fold quotients : {4,2,2}*32
8-fold quotients : {2,2,3}*24
12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,2,12}*384, {8,4,6}*384a, {16,2,6}*384
3-fold covers : {8,2,18}*576, {24,2,6}*576, {8,6,6}*576a, {8,6,6}*576c
4-fold covers : {8,4,6}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,2,24}*768, {8,4,12}*768a, {16,4,6}*768a, {16,4,6}*768b, {16,2,12}*768, {32,2,6}*768, {8,4,6}*768c
5-fold covers : {40,2,6}*960, {8,10,6}*960, {8,2,30}*960
6-fold covers : {8,4,18}*1152a, {8,12,6}*1152b, {8,12,6}*1152c, {24,4,6}*1152a, {8,2,36}*1152, {8,6,12}*1152b, {8,6,12}*1152c, {24,2,12}*1152, {16,2,18}*1152, {16,6,6}*1152a, {16,6,6}*1152c, {48,2,6}*1152
7-fold covers : {56,2,6}*1344, {8,14,6}*1344, {8,2,42}*1344
9-fold covers : {8,2,54}*1728, {72,2,6}*1728, {24,2,18}*1728, {24,6,6}*1728a, {8,6,18}*1728a, {8,18,6}*1728a, {8,6,6}*1728b, {8,6,18}*1728b, {8,6,6}*1728c, {24,6,6}*1728b, {24,6,6}*1728d, {24,6,6}*1728e, {8,6,6}*1728e, {24,6,6}*1728f, {8,6,6}*1728f, {8,6,6}*1728g
10-fold covers : {8,4,30}*1920a, {8,20,6}*1920a, {40,4,6}*1920a, {8,2,60}*1920, {8,10,12}*1920, {40,2,12}*1920, {16,2,30}*1920, {16,10,6}*1920, {80,2,6}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14);;
s3 := ( 9,13)(10,11)(12,14);;
poly := Group([s0,s1,s2,s3]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(14)!(2,3)(4,5)(6,7);
s1 := Sym(14)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(14)!(11,12)(13,14);
s3 := Sym(14)!( 9,13)(10,11)(12,14);
poly := sub<Sym(14)|s0,s1,s2,s3>;

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

```

to this polytope