Polytope of Type {2,9,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,4}*288
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 4
Schlafli Type : {2,9,4}
Number of vertices, edges, etc : 2, 18, 36, 8
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,9,4,2} of size 576
   {2,9,4,4} of size 1152
   {2,9,4,6} of size 1728
Vertex Figure Of :
   {2,2,9,4} of size 576
   {3,2,9,4} of size 864
   {4,2,9,4} of size 1152
   {5,2,9,4} of size 1440
   {6,2,9,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,9,4}*144
   3-fold quotients : {2,3,4}*96
   4-fold quotients : {2,9,2}*72
   6-fold quotients : {2,3,4}*48
   12-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,9,8}*576, {2,18,4}*576
   3-fold covers : {2,27,4}*864, {6,9,4}*864, {2,9,12}*864
   4-fold covers : {2,9,8}*1152, {2,36,4}*1152b, {4,18,4}*1152a, {2,18,4}*1152b, {2,36,4}*1152c, {2,18,8}*1152b, {2,18,8}*1152c, {4,9,4}*1152
   5-fold covers : {2,45,4}*1440
   6-fold covers : {2,27,8}*1728, {2,54,4}*1728, {2,9,24}*1728, {6,9,8}*1728, {6,18,4}*1728a, {6,18,4}*1728b, {2,18,12}*1728a, {2,18,12}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope