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# Polytope of Type {2,4,9}

Atlas Canonical Name : {2,4,9}*288
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 4
Schlafli Type : {2,4,9}
Number of vertices, edges, etc : 2, 8, 36, 18
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,9,2} of size 576
{2,4,9,4} of size 1152
{2,4,9,6} of size 1728
Vertex Figure Of :
{2,2,4,9} of size 576
{3,2,4,9} of size 864
{4,2,4,9} of size 1152
{5,2,4,9} of size 1440
{6,2,4,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,9}*144
3-fold quotients : {2,4,3}*96
4-fold quotients : {2,2,9}*72
6-fold quotients : {2,4,3}*48
12-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,9}*576b, {2,8,9}*576, {2,4,18}*576
3-fold covers : {2,4,27}*864, {6,4,9}*864, {2,12,9}*864
4-fold covers : {4,4,9}*1152b, {2,8,9}*1152, {4,8,9}*1152, {8,4,9}*1152, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c
5-fold covers : {10,4,9}*1440, {2,4,45}*1440
6-fold covers : {4,4,27}*1728b, {2,8,27}*1728, {2,4,54}*1728, {12,4,9}*1728, {2,24,9}*1728, {6,8,9}*1728, {4,12,9}*1728, {6,4,18}*1728b, {2,12,18}*1728a, {2,12,18}*1728b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)(12,47)
(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)(23,60)
(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)(34,69)
(35,72)(36,71)(37,74)(38,73);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,31)(16,33)(17,32)(18,34)(19,27)
(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(40,41)(43,47)(44,49)(45,48)
(46,50)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)
(61,72)(62,74);;
s3 := ( 3,15)( 4,16)( 5,18)( 6,17)( 7,23)( 8,24)( 9,26)(10,25)(11,19)(12,20)
(13,22)(14,21)(27,31)(28,32)(29,34)(30,33)(37,38)(39,51)(40,52)(41,54)(42,53)
(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)(49,58)(50,57)(63,67)(64,68)(65,70)
(66,69)(73,74);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*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(74)!(1,2);
s1 := Sym(74)!( 3,40)( 4,39)( 5,42)( 6,41)( 7,44)( 8,43)( 9,46)(10,45)(11,48)
(12,47)(13,50)(14,49)(15,52)(16,51)(17,54)(18,53)(19,56)(20,55)(21,58)(22,57)
(23,60)(24,59)(25,62)(26,61)(27,64)(28,63)(29,66)(30,65)(31,68)(32,67)(33,70)
(34,69)(35,72)(36,71)(37,74)(38,73);
s2 := Sym(74)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,31)(16,33)(17,32)(18,34)
(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(40,41)(43,47)(44,49)
(45,48)(46,50)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)
(60,73)(61,72)(62,74);
s3 := Sym(74)!( 3,15)( 4,16)( 5,18)( 6,17)( 7,23)( 8,24)( 9,26)(10,25)(11,19)
(12,20)(13,22)(14,21)(27,31)(28,32)(29,34)(30,33)(37,38)(39,51)(40,52)(41,54)
(42,53)(43,59)(44,60)(45,62)(46,61)(47,55)(48,56)(49,58)(50,57)(63,67)(64,68)
(65,70)(66,69)(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope