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# Polytope of Type {6,2,4,2}

Atlas Canonical Name : {6,2,4,2}*192
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 5
Schlafli Type : {6,2,4,2}
Number of vertices, edges, etc : 6, 6, 4, 4, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,4,2,2} of size 384
{6,2,4,2,3} of size 576
{6,2,4,2,4} of size 768
{6,2,4,2,5} of size 960
{6,2,4,2,6} of size 1152
{6,2,4,2,7} of size 1344
{6,2,4,2,9} of size 1728
{6,2,4,2,10} of size 1920
Vertex Figure Of :
{2,6,2,4,2} of size 384
{3,6,2,4,2} of size 576
{4,6,2,4,2} of size 768
{3,6,2,4,2} of size 768
{4,6,2,4,2} of size 768
{4,6,2,4,2} of size 768
{4,6,2,4,2} of size 1152
{6,6,2,4,2} of size 1152
{6,6,2,4,2} of size 1152
{6,6,2,4,2} of size 1152
{9,6,2,4,2} of size 1728
{3,6,2,4,2} of size 1728
{6,6,2,4,2} of size 1728
{10,6,2,4,2} of size 1920
{4,6,2,4,2} of size 1920
{5,6,2,4,2} of size 1920
{6,6,2,4,2} of size 1920
{5,6,2,4,2} of size 1920
{5,6,2,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,4,2}*96, {6,2,2,2}*96
3-fold quotients : {2,2,4,2}*64
4-fold quotients : {3,2,2,2}*48
6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,4,2}*384, {6,2,4,4}*384, {6,4,4,2}*384, {6,2,8,2}*384
3-fold covers : {18,2,4,2}*576, {6,2,12,2}*576, {6,2,4,6}*576a, {6,6,4,2}*576a, {6,6,4,2}*576c
4-fold covers : {6,4,4,4}*768, {12,4,4,2}*768, {12,2,4,4}*768, {6,2,4,8}*768a, {6,2,8,4}*768a, {6,4,8,2}*768a, {6,8,4,2}*768a, {6,2,4,8}*768b, {6,2,8,4}*768b, {6,4,8,2}*768b, {6,8,4,2}*768b, {6,2,4,4}*768, {6,4,4,2}*768a, {12,2,8,2}*768, {24,2,4,2}*768, {6,2,16,2}*768, {6,4,4,2}*768d
5-fold covers : {6,2,20,2}*960, {6,2,4,10}*960, {6,10,4,2}*960, {30,2,4,2}*960
6-fold covers : {18,2,4,4}*1152, {18,4,4,2}*1152, {6,4,4,6}*1152, {6,6,4,4}*1152b, {6,6,4,4}*1152c, {6,2,4,12}*1152a, {6,2,12,4}*1152a, {6,4,12,2}*1152, {6,12,4,2}*1152a, {6,12,4,2}*1152c, {36,2,4,2}*1152, {12,2,4,6}*1152a, {12,6,4,2}*1152b, {12,6,4,2}*1152c, {12,2,12,2}*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 : {6,2,28,2}*1344, {6,2,4,14}*1344, {6,14,4,2}*1344, {42,2,4,2}*1344
9-fold covers : {54,2,4,2}*1728, {18,2,12,2}*1728, {6,2,36,2}*1728, {6,6,12,2}*1728a, {6,2,4,18}*1728a, {6,18,4,2}*1728a, {18,2,4,6}*1728a, {18,6,4,2}*1728a, {6,6,4,2}*1728b, {18,6,4,2}*1728b, {6,6,4,2}*1728c, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,6,4,6}*1728a, {6,6,12,2}*1728e, {6,6,4,6}*1728c, {6,2,12,6}*1728c, {6,6,4,2}*1728h, {6,6,12,2}*1728f, {6,2,4,6}*1728, {6,6,4,2}*1728j, {6,6,4,2}*1728k
10-fold covers : {30,2,4,4}*1920, {30,4,4,2}*1920, {6,4,4,10}*1920, {6,10,4,4}*1920, {6,2,4,20}*1920, {6,2,20,4}*1920, {6,4,20,2}*1920, {6,20,4,2}*1920, {60,2,4,2}*1920, {12,2,4,10}*1920, {12,10,4,2}*1920, {12,2,20,2}*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 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (8,9);;
s3 := ( 7, 8)( 9,10);;
s4 := (11,12);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope