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# Polytope of Type {2,3,2,2,4}

Atlas Canonical Name : {2,3,2,2,4}*192
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 6
Schlafli Type : {2,3,2,2,4}
Number of vertices, edges, etc : 2, 3, 3, 2, 4, 4
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,2,2,4,2} of size 384
{2,3,2,2,4,3} of size 576
{2,3,2,2,4,4} of size 768
{2,3,2,2,4,6} of size 1152
{2,3,2,2,4,3} of size 1152
{2,3,2,2,4,6} of size 1152
{2,3,2,2,4,6} of size 1152
{2,3,2,2,4,9} of size 1728
{2,3,2,2,4,4} of size 1728
{2,3,2,2,4,6} of size 1728
{2,3,2,2,4,10} of size 1920
Vertex Figure Of :
{2,2,3,2,2,4} of size 384
{3,2,3,2,2,4} of size 576
{4,2,3,2,2,4} of size 768
{5,2,3,2,2,4} of size 960
{6,2,3,2,2,4} of size 1152
{7,2,3,2,2,4} of size 1344
{9,2,3,2,2,4} of size 1728
{10,2,3,2,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,2,4,4}*384, {2,3,2,2,8}*384, {2,6,2,2,4}*384
3-fold covers : {2,9,2,2,4}*576, {2,3,2,2,12}*576, {2,3,2,6,4}*576a, {2,3,6,2,4}*576, {6,3,2,2,4}*576
4-fold covers : {2,3,2,4,8}*768a, {2,3,2,8,4}*768a, {2,3,2,4,8}*768b, {2,3,2,8,4}*768b, {2,3,2,4,4}*768, {2,3,2,2,16}*768, {2,6,2,4,4}*768, {2,6,4,2,4}*768a, {4,6,2,2,4}*768a, {2,12,2,2,4}*768, {2,6,2,2,8}*768, {2,3,4,2,4}*768, {4,3,2,2,4}*768
5-fold covers : {2,3,2,2,20}*960, {2,3,2,10,4}*960, {2,15,2,2,4}*960
6-fold covers : {2,9,2,4,4}*1152, {6,3,2,4,4}*1152, {2,3,6,4,4}*1152, {2,3,2,4,12}*1152a, {2,3,2,12,4}*1152a, {2,9,2,2,8}*1152, {2,3,2,6,8}*1152, {2,3,6,2,8}*1152, {6,3,2,2,8}*1152, {2,3,2,2,24}*1152, {2,18,2,2,4}*1152, {2,6,2,6,4}*1152a, {2,6,6,2,4}*1152a, {2,6,6,2,4}*1152c, {6,6,2,2,4}*1152a, {6,6,2,2,4}*1152b, {2,6,2,2,12}*1152
7-fold covers : {2,3,2,2,28}*1344, {2,3,2,14,4}*1344, {2,21,2,2,4}*1344
9-fold covers : {2,27,2,2,4}*1728, {2,9,2,2,12}*1728, {2,3,2,2,36}*1728, {2,3,2,18,4}*1728a, {2,9,2,6,4}*1728a, {2,9,6,2,4}*1728, {6,9,2,2,4}*1728, {2,3,6,2,4}*1728, {2,3,6,6,4}*1728a, {6,3,2,2,4}*1728, {2,3,2,6,12}*1728a, {2,3,2,6,12}*1728b, {2,3,6,2,12}*1728, {6,3,2,2,12}*1728, {6,3,2,6,4}*1728a, {6,3,6,2,4}*1728, {2,3,2,6,12}*1728c, {2,3,6,6,4}*1728d, {2,3,2,6,4}*1728
10-fold covers : {2,15,2,4,4}*1920, {2,3,2,4,20}*1920, {2,3,2,20,4}*1920, {2,15,2,2,8}*1920, {2,3,2,10,8}*1920, {2,3,2,2,40}*1920, {2,30,2,2,4}*1920, {2,6,2,10,4}*1920, {2,6,10,2,4}*1920, {10,6,2,2,4}*1920, {2,6,2,2,20}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := (6,7);;
s4 := ( 9,10);;
s5 := ( 8, 9)(10,11);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(1,2);
s1 := Sym(11)!(4,5);
s2 := Sym(11)!(3,4);
s3 := Sym(11)!(6,7);
s4 := Sym(11)!( 9,10);
s5 := Sym(11)!( 8, 9)(10,11);
poly := sub<Sym(11)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s1*s2*s1*s2,
s4*s5*s4*s5*s4*s5*s4*s5 >;

```

to this polytope