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# Polytope of Type {2,4,9,2}

Atlas Canonical Name : {2,4,9,2}*288
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 5
Schlafli Type : {2,4,9,2}
Number of vertices, edges, etc : 2, 4, 18, 9, 2
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,9,2,2} of size 576
{2,4,9,2,3} of size 864
{2,4,9,2,4} of size 1152
{2,4,9,2,5} of size 1440
{2,4,9,2,6} of size 1728
Vertex Figure Of :
{2,2,4,9,2} of size 576
{3,2,4,9,2} of size 864
{4,2,4,9,2} of size 1152
{5,2,4,9,2} of size 1440
{6,2,4,9,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,9,2}*576, {2,4,18,2}*576b, {2,4,18,2}*576c
3-fold covers : {2,4,27,2}*864, {2,4,9,6}*864
4-fold covers : {4,4,9,2}*1152a, {2,4,36,2}*1152b, {2,4,36,2}*1152c, {2,4,18,4}*1152c, {4,4,9,2}*1152b, {2,8,9,2}*1152, {2,4,18,2}*1152, {2,4,9,4}*1152a
5-fold covers : {2,4,45,2}*1440
6-fold covers : {2,4,27,2}*1728, {2,4,54,2}*1728b, {2,4,54,2}*1728c, {2,4,9,6}*1728, {2,4,18,6}*1728c, {2,4,18,6}*1728d, {2,4,18,6}*1728e, {2,12,9,2}*1728, {2,12,18,2}*1728c, {6,4,9,2}*1728
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)(27,35)
(29,36)(31,37);;
s2 := ( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)(20,26)
(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);;
s3 := ( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)(17,18)
(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);;
s4 := (39,40);;
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*s1*s0*s1,
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*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(40)!(1,2);
s1 := Sym(40)!( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)
(27,35)(29,36)(31,37);
s2 := Sym(40)!( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)
(20,26)(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);
s3 := Sym(40)!( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)
(17,18)(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);
s4 := Sym(40)!(39,40);
poly := sub<Sym(40)|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*s1*s0*s1, 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*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope