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

Atlas Canonical Name : {4,3,2,2}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 5
Schlafli Type : {4,3,2,2}
Number of vertices, edges, etc : 8, 12, 6, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,2,2,2} of size 384
{4,3,2,2,3} of size 576
{4,3,2,2,4} of size 768
{4,3,2,2,5} of size 960
{4,3,2,2,6} of size 1152
{4,3,2,2,7} of size 1344
{4,3,2,2,9} of size 1728
{4,3,2,2,10} of size 1920
Vertex Figure Of :
{2,4,3,2,2} of size 384
{4,4,3,2,2} of size 768
{6,4,3,2,2} of size 1152
{10,4,3,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3,2,2}*96
4-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,2,4}*384, {8,3,2,2}*384, {4,6,2,2}*384
3-fold covers : {4,9,2,2}*576, {4,3,2,6}*576, {4,3,6,2}*576, {12,3,2,2}*576
4-fold covers : {8,3,2,2}*768, {4,3,2,8}*768, {8,3,2,4}*768, {4,12,2,2}*768b, {4,6,2,2}*768b, {4,6,2,4}*768, {4,6,4,2}*768b, {4,12,2,2}*768c, {8,6,2,2}*768b, {8,6,2,2}*768c, {4,3,4,2}*768
5-fold covers : {4,3,2,10}*960, {4,15,2,2}*960
6-fold covers : {4,9,2,4}*1152, {8,9,2,2}*1152, {4,18,2,2}*1152, {4,3,2,12}*1152, {12,3,2,4}*1152, {24,3,2,2}*1152, {8,3,2,6}*1152, {8,3,6,2}*1152, {4,3,6,4}*1152, {4,6,2,6}*1152, {4,6,6,2}*1152a, {4,6,6,2}*1152b, {12,6,2,2}*1152a, {12,6,2,2}*1152b
7-fold covers : {4,3,2,14}*1344, {4,21,2,2}*1344
9-fold covers : {4,27,2,2}*1728, {4,3,2,18}*1728, {4,9,2,6}*1728, {4,9,6,2}*1728, {12,9,2,2}*1728, {4,3,6,6}*1728a, {4,3,6,2}*1728, {12,3,2,2}*1728, {4,3,6,6}*1728b, {12,3,2,6}*1728, {12,3,6,2}*1728
10-fold covers : {4,3,2,20}*1920, {8,3,2,10}*1920, {4,15,2,4}*1920, {8,15,2,2}*1920, {4,6,2,10}*1920, {4,6,10,2}*1920a, {20,6,2,2}*1920a, {4,30,2,2}*1920
Permutation Representation (GAP) :
```s0 := (4,6);;
s1 := (3,4)(5,6);;
s2 := (1,3)(2,5);;
s3 := (7,8);;
s4 := ( 9,10);;
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,
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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope