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

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

```

to this polytope