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

Atlas Canonical Name : {4,3,4,2}*192
if this polytope has a name.
Group : SmallGroup(192,1538)
Rank : 5
Schlafli Type : {4,3,4,2}
Number of vertices, edges, etc : 4, 6, 6, 4, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,4,2,2} of size 384
{4,3,4,2,3} of size 576
{4,3,4,2,4} of size 768
{4,3,4,2,5} of size 960
{4,3,4,2,6} of size 1152
{4,3,4,2,7} of size 1344
{4,3,4,2,9} of size 1728
{4,3,4,2,10} of size 1920
Vertex Figure Of :
{2,4,3,4,2} of size 384
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,4,2}*384a, {4,3,4,2}*384b, {4,6,4,2}*384d, {4,6,4,2}*384e, {4,6,4,2}*384f, {4,6,4,2}*384g
3-fold covers : {4,9,4,2}*576
4-fold covers : {4,3,4,4}*768a, {4,3,4,4}*768b, {4,12,4,2}*768f, {4,12,4,2}*768g, {4,12,4,2}*768h, {4,12,4,2}*768i, {4,3,8,2}*768, {8,3,4,2}*768, {4,3,4,2}*768, {4,6,4,2}*768c, {4,6,4,2}*768d, {4,6,4,2}*768e, {4,6,4,2}*768f
5-fold covers : {4,15,4,2}*960
6-fold covers : {4,9,4,2}*1152a, {4,9,4,2}*1152b, {4,18,4,2}*1152d, {4,18,4,2}*1152e, {4,18,4,2}*1152f, {4,18,4,2}*1152g, {4,3,4,6}*1152, {4,3,12,2}*1152, {4,6,12,2}*1152f, {12,3,4,2}*1152, {12,6,4,2}*1152f
7-fold covers : {4,21,4,2}*1344
9-fold covers : {4,27,4,2}*1728
10-fold covers : {4,3,4,10}*1920, {4,6,20,2}*1920c, {20,6,4,2}*1920c, {4,15,4,2}*1920a, {4,15,4,2}*1920b, {4,30,4,2}*1920d, {4,30,4,2}*1920e, {4,30,4,2}*1920f, {4,30,4,2}*1920g
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 6)( 4, 5)( 7,14)( 8,15)( 9,10)(11,13)(12,16);;
s1 := ( 2, 4)( 3, 7)( 6,11)( 9,14)(10,13)(12,15);;
s2 := ( 3, 8)( 4, 5)( 6,15)( 9,16)(10,12)(11,13);;
s3 := ( 1, 8)( 2,15)( 3, 7)( 4,12)( 5,16)( 6,14)( 9,11)(10,13);;
s4 := (17,18);;
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, 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,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!( 1, 2)( 3, 6)( 4, 5)( 7,14)( 8,15)( 9,10)(11,13)(12,16);
s1 := Sym(18)!( 2, 4)( 3, 7)( 6,11)( 9,14)(10,13)(12,15);
s2 := Sym(18)!( 3, 8)( 4, 5)( 6,15)( 9,16)(10,12)(11,13);
s3 := Sym(18)!( 1, 8)( 2,15)( 3, 7)( 4,12)( 5,16)( 6,14)( 9,11)(10,13);
s4 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, 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, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2 >;

```

to this polytope