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

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

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

```

to this polytope